Well, I've had two more random thoughts about English evolution (so far) today.
First, I realized that there is already a mechanism in common use for English to lose the past tense entirely. Figure it out, yet? I just used it. English has come to like to move auxiliary verbs ("do"/"did") before the subject in questions, e.g. "Did you figure it out, yet?" However, it's becoming common use to drop auxiliary verbs in English. This is one such case. As the auxiliary verb, not the main verb, carries the tense, this change leads to a loss of explicitly stated tense.
In the case of questions, the main verb is kept in the infinitive, which is identical in form to the present tense. Languages have a way of evolving based on analogy. It's not impossible that this could be applied to verbs in general, losing the past tense entirely (or at least a distinct form for the past tense; it's possible a periphrastic form, like "do"/"did" would then take it's place in all cases).
The third thought of the day came from me pondering the second one. This modern tendency to drop auxiliary verbs and sometimes the subject is not unique to questions. It's also applied to the perfect (e.g. "I've been" -> "Been") and the progressive (e.g. "I'm thinking" -> "Thinking"). If the latter case became the standard, the effect would basically be the same as with dropping "do"/"did". However, if the former occurred, it could result in the past participle replacing other forms, such as the perfect or past tense.
Here's where my random thought came in: the possibility of replacing the past tense is especially interesting, because it may have happened before in English. If you look back at Old English, you'll notice there are two distinct forms - past tense and past participle - for both strong verbs, which retain this distinction (verbs like "write"/"wrote"/"written"), as well as weak verbs (what became our modern regular verbs like "poke"/"poked"). The past tense for weak verbs, in Old English, was -de. Care to guess what the past participle was? It's -ed, the modern past tense suffix. In summary, the Old English part participle has become the modern English past tense form.