What are some "easy" unreasonable implications of O(1) time memory access?
Memory access is assumed to be constant time, because normally you access memory that is close to each other, eg. from one hard drive or one given computer. Under that assumption there is a constant maximum amount of time to retrieve that data.

You are right. If I access data randomly accross very large amounts of data, then it's nowhere near constant, but normally you can arrange the data beforehand in a way that makes it O(1), because of it fitting onto one machine or very close machines. Another reason is that, harddrives all come with their hardware. That means normally you won't be switching hard drives in and out of one machine, and each drive comes with it's own reader. Also most machines are limited to a certain amount of drives. Those technical limitation give O(1) comlexity to most pratical applications and the software perspective of things.

One easy and unreasonable implication of O(1) time memory access is violating the assumptions above by scattering data randomly, across multiple machines in an unordered fashion or switching drives in and out of machines and expecting O(1) access times. Anything relying on wrong assumption is doomed to be wrong and thus unreasonable.