They used to in AD&D. I wonder 5E does not. What problems do you see?
One of the issues in 2e was the interaction between specialization schools and opposition schools. For example,
avoidance was both Abjuration and Alteration (now known as Transmutation), and those schools were opposition schools. Could an abjurer learn this spell? Would they get specialization bonuses with it? At the time of the 2e core rules, this was not a
huge problem (
avoidance, at 5th level, was the first spell I could find that belonged to opposing schools), but as more spells, and particularly "parallel schools" (e.g. Artifice from Spells & Magic) were added it became bigger. I believe the ruling was that opposition schools overruled specialization schools (so neither an abjurer nor a transmuter could learn
avoidance, but it's not exactly obvious.
This particular issue does not exist in 5e since specialists no longer have opposition schools, but similar issues do, or at least could do. For example, a demiplane created by a master of illusions may have an "ephemereal" trait that makes illusions harder to distinguish (disadvantage on saves vs illusions) but energies less intense (advantage on saves vs evocations). In a dual-school world, you could easily argue that
color spray ought to be both illusion and evocation (on account of dazzling lights) - so would you get advantage or disadvantage on it? Or would they cancel out? Again, not an insurmountable problem, but keeping each spell to a single school solves it before it happens.