In my opinion, Dominion actually has far too many types. I think there should be only Action, Treasure, Night, Victory. And Curse, I suppose, although rules-wise that would have worked fine as a Victory type instead.
I feel the opposite! Types let you refer to the types. This both lets you deal with problems, and lets you make cards that work with a category in the simplest way. The cost is just a word on that bottom bar; it does not feel high. A good example is, multiple cards would have liked to exempt Throne Rooms or one-shots. This would be trivial if they had types. It's essentially impossible given that they don't.
The ability of players to refer to the group is also nice. It's nice in the rulebooks too, even when there aren't special rules.
Of all existing types, conceivably I could have done without Gathering (living with those interactions). The others all feel like they're pulling their weight.
All the other types are fundamentally different from those 4 or 5. Those ones are really needed; they tell you what you can do with the card and when (when you can play it; or if you can play it). Things like attack could have been a keyword instead; this was dicussed somewhere else recently.
Duration doesn't have any meaningful rules associated with it; all cards are cleaned up on that last turn in which they do something. It just so happens that for regular actions, that's the same turn they were played. It's not clear from the rulebooks if Reaction actually has special rules. For both of those, I can see how the color is helpful, though. Although Temporum did fine with having "until-next-turn" cards just stay out without any special type.
I've said before that I'm against Reserve being a type. It's not even clear what that type means. Not that it can be called (Distant Lands). Not that it uses the Tavern Mat (Miser/Copper). The color doesn't seem particularly meaningful; because you know that stuff on your Tavern Mat is stuff to pay attention to at special times (except when Copper ends up there. Or Distant Lands).
"Attack" could be a word in the middle of card text, and that does have some benefits; I don't think anything else can benefit from that approach. Mid-text Attack is handling two things: attacks that are optional, and attacks timed at other than when playing a card (e.g. Ill-Gotten Gains). Arguably I shouldn't have done optional attacks - they're political (yes you can draw two terminals and choose to play the attack or not, but getting rid of some of the politics is still a positive). I don't know how much trouble "let you Moat Ill-Gotten Gains" is worth.
Duration was not originally a type, and Greed also has those cards without a special type. But there is in fact a lot of value to the color there, ditto for Reactions. Reactions originally had rules associated with them, and that version was better (they could be played at a special time).
Reserve cards put themselves on your Tavern mat. It seemed helpful at the time and I mean no regrets.