I don't think you should change any types unless you can give a solid reason for doing so. As Worldslayer said, types and abilities are some of the core components that define a 'mon. Why change that which doesn't need to be changed?
I'm also going to go one step further and say that I don't think you - or any other designer/developer - should change something "just because". Any changes you make in a Pokémon game's core components - types, abilities, base stats, et cetera - must be for the benefit of the game, not for the creator to prove something. (This applies to any form of game design & development, not just Pokémon.)
When thinking about making changes to the fundamentals, I think you should ask yourself these two questions:
• Will this change improve the audience's experience when playing?
• Will the average player understand why I made this change?
To use an example of yours, what will the average player gain from Alakazam being Electric-type? I don't believe it makes sense for Alakazam to be anything other than pure Psychic: it already has a decent move pool, good stats, and a Mega Evolution to boot, making it even more powerful in a well-built team. Plus, it isn't Electric-themed at all.
Short version: Don't fix what doesn't need to be fixed, and make sure you have a solid reason for everything you do.