I think they matter! But you say "other than for thematic reasons..." so maybe not. So my answer may not apply, but I want to give it anyway in the hopes that gets other users thinking about power sources and why they are cool.
Here's some examples we've used:
You can use power sources to put thematic handles on things.
One of the adventure groups we set up last year was "the PCs are all students at a magic academy." How to do it? We simply made it a requirement that all of the PCs had the Arcane power source. All roles were covered- strikers, defenders, controllers, leaders.. were all in there.
Another handle: I have an "All Drow" group- an underdark house-- although it's reaching a bit outside of canon, we thought it would be cool that only female drow PCs could have the divine power source. Because Lolth only truly blesses female characters.
Finally: Dark Sun - no divine character classes, but still the roles can get filled.
Thematically, that really has an effect on the campaign.
Adventure-wise- as a DM the power sources are great ways to shine a spotlight on different types of characters. We've definitely had games where a PC had to have a certain power source in order to attempt a certain task. For example, in one game, the PCs had to recruit, train, and lead a militia.. it's a diplomacy check, but I further restricted it to "martial characters only", because I assumed martial characters would not only have the necessary experience, they'd have "cred". Cleansing a shrine might require a divine source, speaking to an ancient elemental- maybe primal. Attempting to interface with an intelligent alien crystal in a dungeon? Maybe that's arcane or psionic only.
So "other than thematically"..maybe not? But thematically, definitely!