I'm sorry, but in questions of language, and especially of language change, "why" questions don't usually have answers, other than "because that's what happened".
The Early Modern English forms you give had already changed - in Old English, the pattern was very like modern German, but the distinct plural forms had mostly dropped out of use before Shakespeare's time (you still find ye goeth in the King James Bible).
The remaining distinctions are -est and -eth vs -s. The first of these disappeared when thou disappeared. The second was a dialect difference: IIRC -s was Northern, and -eth was Southern, though it may have been more complicated than that.
Edited to remove a wrong claim.
In the journey from Old English to what we write today, the ash (Æ) tended to metamorphose into a simple E and various "ae" forms got reduced to just "e": Ælfwyn became Elvin, Æthelræd became Ethelred, aether and aesthetic became ether and esthetic (except when @Cerb spells them), and so on. The distinction was simply planed off over the centuries. When there was no need for the superfluous Æ (because its sound was rendered with a single letter) it got dialed way down in frequency. The same thing happened, more or less, with the thorn (Þ, þ) and eth (Ð, ð) characters, because the th digraph supplanted them.
An even more obvious influence involved the printing press. In the early days of typography, fonts were imported from Germany and Italy, and those countries did not use the oddball English characters, so substitutes had to be found. "E" substituted quite nicely for the ash, and "Y" for the thorn (as we see on the signs in front of all those cutesy Ye Old Whatever shops).
Elaboration
Asked for citations, I lazily looked to the Web first, but real scholarship in this matter is difficult to Google. Here are some not-stringently-academic citations, together with a disclaimer.
The thorn was particularly popular as a sign for 'th' in Medieval English, but with the advent of printing came a problem. There was no thorn sign in the printing fonts, as they were usually cast outside of England. So, since the sign for thorn slightly resembled the lower-case 'y', that's what was substituted.
The thorn continued to be used, but printing caused its eventual demise from the English alphabet. As mentioned earlier, lingering proof of its existence hangs on in the outmoded 'Ye'.
Thorn — Missing Letter of the Alphabet (reposted with correct glyphs here).
Ultimately, the letter was abandoned when printing began to streamline the alphabet and eliminate unnecessary letters. Æ was separated into AE, and the language moved on. However, you can still find ash used stylistically in names like Encyclopædia Britannica and ÆON.
Mighty Markup.
Disclaimer: I feel it only fair to point out that the reference books I have at hand (printed versions, so no linky-link), suggest that the ash (or æsc in OE), was pretty much gone by 1250 due to the influence of Norman French. This was a couple hundred years before the invention of the printing press, so we cannot accept that as the proximal cause. Still, Gutenberg almost certainly put the nail in the coffin of that and the other oddball characters (including wynn and yogh — look those up for your amusement and edification sometime).
Best Answer
From a linguistic and phonetics standpoint, in the majority of cases, the suffix -t as a formative of past participle of verbs appeared as a result of the reduction of -ed to -'d, and the devocalization of d.
Here is the full explanation from OED with some historical notes:
OED has a separate entry for the suffix -t as a formative of the past tense of some weak verbs and adds that: "In modern English on the contrary the spelling in t is more frequent in the past participle, esp. when used adjectivally, than in the past tense: cf. tempest-tost (see tempest-tossed adj.), the wind tossed the ship; in time past, he passed his time."
Additionally, it is not only used in British English. For example, shortening of a long vowel in the participle of certain verbs, as in crept, slept, the spelling with -t is universal.