Because telegraph was a manually routed transmission. Like the original Ethernet of the 1980's, one had long cable runs with stations tapping the cable along its length. Transmission to another station on the same cable run was single hop, but to a station on another cable run would be multi-hop.
Unlike Ethernet however, with it's automatic repeaters, telegraph had manual repeaters who would receive a message on one cable and retransmit it on another. For a Trans-Atlantic transmision this might involve several hops on each side of the trans-Atlantic cable:
Evanston to Chicago
Chicago to New York
New York to Belfast
Belfast to London
London to Paris
Paris to Rheims
Rheims to Verdun
In all these retransmits, there was a very real danger that single punctuation marks might get missed, thus garbling the message. By introducing distinct words such as STOP, COMMA, SEMICOLON for the punctuation marks a degree of redundancy - essentially error-checking - was introduced that made such errors vastly less likely.
That it was the military that first made this practice standard is not surprising. When giving orders, competent commanders go to great lengths to ensure that the orders are direct and unambiguous. An example of the consequences of even a simple failure, two orders arriving out of sequence, is well known from the first days of the 1809 campaign in Bavaria.
Napoleon sent a first message to Berthier from Paris by semaphore, which was delayed for more than a day by cloudy conditions near Strasbourg. Then he sent a second, more detailed, message by courier which arrived to Berthier first. As a consequence of the orders arriving out of order (but not being recognized as such), Berthier took the more general instructions as an amendment of the detail rather than the other way around - resulting in Davout's corps remaining at Regensburg two days longer than intended by Napoleon.
The ensuing correspondence between Berther and Davout is well described in Volume 1 of John H Gill's Thunder on the Danube, as the two marshals attempt to sort out, long distance, the true intent of Napoleon's orders.
Why only puncutation you might ask? Because normal language already contains a great deal of redundancy, both in spelling and grammar, as evidenced here:
Finally - why were English words used instead of special code? Because the sender was charged for the message by the "word" - and every character of a "special code" was it's own word. And why was that you ask - because words can be processed faster and more accurately than special codes. Words, as noted above, contain error-checking redundancy that special codes cannot. The difficulty is not at the sending end so much as at the receiving end, where the receiver cannot utilize any obvious redundancy to ensure accuracy.
The consequential combination of both lower cost and improved accuracy (the whole point of replacing single character punctuation after all) meant it was never going to be useful, in the large, to use special codes rather than words.
Further examples of telegraphese and commercial (telegraph) code aimed at both decreasing cost and improving clarity and accuracy of telegraphed messages..