The original poster has asked what seems like a reasonable question, but the answer follows a different train of thought. One could easily use methanol in an SN1 reaction in place of ethanol. It would work as expected.
When one studies organic chemistry and the reactions in textbooks, the purpose of a given reaction isn't always explained. One does not do SN1 reactions in ethanol in a desire to prepare an ethyl ether, especially as E1 reactions compete. Usually, there are better ways. So ethanol or methanol are not being chosen as the preferred reaction to prepare a methyl or ethyl ether. The solvents are chosen to study the reactions themselves. The most sought after value is generally the reaction rate. So, the solvent choice is to compare different reactions, is A faster than B? Even though a slow reaction could be accelerated in methanol, how would you compare B (methanol) is faster than A (ethanol).
Perhaps a better question might be why might one chose ethanol rather than methanol to study reaction rates? I can think of several reasons.