According to the Nadistuti Sukta (Sanskrit: नदिस्तुति सूक्त), "hymn of praise of rivers", which is hymn 10.75 of the Rigveda:
There were 25 rivers and the most important was the Sindhu river and the sacred river was the Sarasvati since the Vedic people were living in the valleys of the Sindhu river (Sapthsandhav Pradesh) and near the Sarasvati river; and later, the Mahabharata mentions that the Sarasvati dried up in a desert.
So my question is:
Is the reason that the Aryans started calling the Ganga a holy river that they moved to the Ganga valley and that the Ganga is the biggest river of Magadh/North India?
During the course of Hindiusm, the local elements played a crucial role in shaping the sacred.
During the Rigvedic Ages, Saraswati and Indus played a crucial role in forming the hymns and myths.
During the Vedic Ages, mainly Upanishads and Puranas, which occurred in the Gangatic Planes, Ganga and it's tributaries gained more prominence and importance. It was in this time when Aryavrat was called 'Sapta-Sindhu' (the land of seven rivers, including Indus and Ganges).
Later as Hinduism spread to Dandakaranya (दण्डकारण्य) and Deccan Plateau, other subcontinental rivers like Narmada, Krishna and Cauveri also gained prominence.
Devi Puraanam, Book 9, Chapter 6
शृणु नारद वक्ष्यामि कथामेतां पुरातनीम् ।
यस्याः श्रवणमात्रेण सर्वपापात्प्रमुच्यते ॥ १६ ॥
लक्ष्मीः सरस्वती गङ्गा तिस्रो भार्या हरेरपि ।
प्रेम्णा समास्तास्तिष्ठन्ति सततं हरिसन्निधौ ॥ १७ ॥
चकार सैकदा गङ्गा विष्णोर्मुखनिरीक्षणम् ।
सस्मिता च सकामा च सकटाक्षं पुनः पुनः ॥ १८ ॥
विभुर्जहास तद्वक्त्रं निरीक्ष्य च क्षणं तदा ।
क्षमां चकार तद्दृष्ट्वा लक्ष्मीर्नैव सरस्वती ॥ १९ ॥
बोधयामास पद्मा तां सत्त्वरूपा च सस्मिता ।
क्रोधाविष्टा च सा वाणी न च शान्ता बभूव ह ॥ २० ॥
O Naarada! listen I am reciting the ancient tale, hearing which, one gets free from all sins. 16.
Lakshmi, Saraswati and Ganga are three beloved wives of Vishnu, and they live together with harmony always close to Hari. 17.
But one day, Ganga, smiling and full of passion, started looking at Vishnu's face and drew continuous side glances on Him. 18.
Vishnu also smiled looking at Her face for moment. Seeing all this, Lakshmi took no offense, but not Saraswati. 19.
Then Lakshmi, who is Sattva incarnate, smilingly consoled Saraswati. But filled with anger Saraswati did not become quiet at all. 20.
सर्वत्र समताबुद्धिः सद्भर्तुः कामिनीं प्रति ।
धर्मिष्ठस्य वरिष्ठस्य विपरीता खलस्य च ॥ २२ ॥
ज्ञातं सौभाग्यमधिकं गङ्गायां ते गदाधर ।
कमलायां च तत्तुल्यं न च किञ्चिन्मयि प्रभो ॥ २३ ॥ गङ्गायाः पद्मया सार्धं प्रीतिश्चास्ति सुसम्मता ।
क्षमां चकार तेनेदं विपरीतं हरिप्रिया ॥ २४ ॥
A good husband, who is religious and well qualified, always have equal liking of all his wives. Only a stupid acts contrary to this. 22.
O Vishnu, holder of Gadaa! Your liking to Ganga is clearly visible, and You have same love for Lakshmi too. Only I am deprived of your love. 23.
This is why, Ganga and Lakshmi like each other. And thus, Lakshmi does not do things against this harmony between them both.
The fight and curse of Saraswati to Ganga
सरस्वतीवचः श्रुत्वा दृष्ट्वा तां कोपसंयुताम् ।
मनसा च समालोच्य स जगाम बहिः सभाम् ॥ २७ ॥
गते नारायणे गङ्गामुवाच निर्भयं रुषा ।
वागधिष्ठातृदेवी सा वाक्यं श्रवणदुष्करम् ॥ २८ ॥
हे निर्लज्जे हे सकामे स्वामिगर्वं करोषि किम् ।
अधिकं स्वामिसौभाग्यं विज्ञापयितुमिच्छसि ॥ २९ ॥
मानचूर्णं करिष्यामि तवाद्य हरिसन्निधौ ।
किं करिष्यति ते कान्तो ममैवं कान्तवल्लभे ॥ ३० ॥
Hearing Saraswati's words and seeing Her full of wrath, Hari thought for a moment and went out of the court. 27.
Narayana gone out, Saraswati, who is main deity of speech, spoke full of anger and fearless to Ganga, things which are hard to hear. 28.
O passionate and shameless Gangaa! being elated with pride of your husband's love, now you are wanting to show that your husband loves you more. 28.
Let me crush down your this pride here in front of Hari. O beloved of husband! let us see, what your husband do to me.
Hearing this speech of Gangaa, Saraswati cursed Her. 41.
You will definitely go to Earth, and take the sins of sinners. Between all this, Bhagawaan came there. 42.
Hari tells Lakshmi, Gangaa and Saraswati, how they shall become rivers on Earth
[Note: here below, Vishnu uses the words "in some parts you become a river" and "in full parts you stay with me" quite often. To understand this read this- "O Lakshmi! in Your part-incarnation(in some parts of Yours) You shall become a river. And in Your full parts (i.e. in whole, completely, in full parts) You shall stay with Me."
I wrote this note, so that reader may not have difficulty in interpreting what is in some parts and in full parts.]
Hearing the reason of fight and curses between them,, Lord Vishnu told the three sorrowful Devis, one by one-
O Auspicious Lakshmi! with some of Your parts, go to DharmaDhwaja's house. 45.
You will be born on Earth without any womb, and become his daughter, and there only, due to misfortune, You will become a tree. 46.
Then You will become wife of ShankhaChuuda, who is Indra of Asuras and who has my parts. After this, You will become my wife again, undoubtedly. 47.
You will be known as Tulasi, who purifies the three world, on the land of Bharata. But for now, with some of Your parts, You become a river and quickly go to  BharataBhumi, due to the curse of Bhaarati(Saraswati), and You will be called Padmaavati river there.
Let Gangaa now go to Shiva's abode and Padmaa(Lakshmi) stay here with Me, as She is calm, never angry, Saatvik and devoted to Me. 45.
So, Saraswati and Ganga fight over Vishnu. Saraswati curses Lakshmi because Lakshmi tries to save Ganga from Saraswati. Ganga curses Saraswati because She cursed Lakshmi without any fault. Then Saraswati in return curses Ganga to be a river. And then Vaasudeva Hari comes to settle down quarrel and directs them how they will incarnate.
Are "aryans" didn't move to ganga valley, the yajur Veda talks mostly about ganga, while rig Veda about saraswati.
Mahabharata mentions saraswati dried up, but before it dried both rivers enjoyed equal prominence in Hinduism, nowadays only ganga remains on earth but slowly it's also being contaminated due to powers of Kali Yuga.
In many Tantras and puranas, saraswati is also called purifying, sin removing river. So both were equally important.
Historically, when (and why) did Ganga become a holy river?
As per scriptures Ganga is heavenly river and is considered as holy river even before Bhagiratha brought it on the Earth. As per Valmiki Ramayana: Balakanda-Sarga 41,
भस्म राशी कृतान् एतान् पावयेत् लोक कांतया |
तया क्लिन्नम् इदम् भस्म गंगया लोक कान्तया |
षष्टिम् पुत्र सहस्राणि स्वर्ग लोकम् गमिष्यति || १-४१-२०
[Garuda said to Amshuman:] World purifier River Ganga will drift them who are rendered as mounds of ashes to heaven, and when she who is much adored by all worlds drenches this ash, that River Ganga herself will lead the sixty-thousand sons of Sagara to heaven.
Later on Sagara, Amshuman, Dileepa tried to bring Ganga on Earth and finally Bhageeratha succeeded.
And this all happened many generations before Lord Shri Rama.
As per Puranas, Rama incarnation happened in 24th Treta Yuga then Ganga is considered the Holy river atleast from 24th Treta Yuga.
As per modern scholars even if Rama incarnation happened in 28th Treta Yuga then also Ganga is considered the Holy river much before Ramayana & Mahabharata time.
Lord Brahma instructed Ganga by saying- ' Ganga! Go to the earth, where you would be known as Gomti. Sage Vashishtha will lead you to your destination. Just follow him like a daughter follows her father.'
Sage Gautam requested Lord Shiva to liberate him from the sins of
killing a cow. He also requested lord Shiva to manifest the stream of
river Ganga that place. This Ganga became famous as Gautami Ganga.