The spoiling of ballots or the casting of blank votes as a protest has not, for the most part, been an effective 'political instrument' of the masses for change.
Although the percentage of spoiled or blank ballots has increased over the past 30 years, the numbers have rarely been dramatic. The main exceptions to this are in the Latin American countries of Peru (2000) and Bolivia (2011). In both countries, voting is compulsory. There's also the interesting case of the 1957 election in Argentina where spoiled ballots arguably damaged the interests of those who cast them.
For the 2000 Peru election:
According to the ONPE’s unverifiable results, nearly thirty percent
(29.93%) of all voters spoiled their ballots, while 51.2% voted for
President Fujimori; 17.68% voted for Toledo, despite his
non-participation; and 1.19% left their ballots blank.
(my highlighting) / ONPE = Oficina Nacional de Procesos Electorales
This followed the withdrawal of presidential candidate Alejandro Toledo who
urged his supporters to boycott the vote or to purposefully spoil
In response, many voters spoiled their ballot papers by writing 'no to fraud' or something similar (pdf).
Numerous protests followed the declaration that Alberto Fujimori had won, and the situation deteriorated further when it was revealed that the ruling party was found to have bribed an opposition congressman. Fujimori finally resigned on November 22. An interim president took over until the election in June 2001 which Toledo won.
The 2nd case, Bolivian judicial election 2011, is a little less clear-cut in terms of effect though the numbers are bigger. In this election 42.9% of ballots were 'Null' and another 14.9% were left blank. For the aftermath,
This represents the first electoral defeat of the Morales
administration. Following the election, media reports were quick to
claim that the elections represented a stark challenge to Morales’
ability to govern.... This victory has revitalized an opposition that
has otherwise struggled to counter balance the MAS electoral machine.
In the Argentine Constitutional Assembly Election of 1957 (pdf), Juan Peron, who had been ousted in 1955, called on voters to cast blank votes. Millions responded - in fact, 'invalid votes' topped the pole with 24.7%, followed by the anti-Peronist UCR-P with 24.2%. The other main party was the UCR-Intransigents with 21.2%. This party's leader Arturo Frondizi had
signaled a willingness to recognize and eventually rehabilitate the
Thus, had Peron not asked voters to cast blank ballots, the party which was holding out an olive branch to Peronists would almost certainly have won. Then,
In 1958...the Peronists and UCR Intransigents did join forces after
Peron endorsed Frondizi four days before the presidential election.
Frondizi won nearly half the popular vote and over two-thirds of the
electoral college votes.
Examples of high percentages of spoilt / blank ballots are most obvious in countries where voting is compulsory; otherwise, people just stay at home. However (pdf),
invalid voting (blanks plus nulls) as [sic] more than doubled since the
1970s and since the year 2000 the average percentage of invalid votes
in national elections across the world has been estimated at 4,3%
Despite this, there is little evidence that spoilt / blank ballots have been effective as a means of protest. Also, many ballots are not intentionally spoilt.
The recent 2018 election in Cambodia saw over 8.5% spoilt ballots, but the international criticism of these elections resulted not from this but rather from the banning of the main opposition party, always an effective way to win an election.
The 1969 and 2017 elections in France also saw high than usual numbers of spoilt ballots but there is little evidence that these had any immediate impact. However,
there is a movement underway for the blank ballots to count as a share
of the overall election vote. According to a recent Ifop poll, 40% of
French voters said they would cast a blank vote if it were recognized
under French law.
If that 40% did indeed cast blank votes, this probably would have an impact, but this remains purely hypothetical for now.