Ahem, I like
being forced to use all possible party members. It's very annoying if a game advertises that there are N playable characters, but when I play the game, I have no incentive to use anything but my A team, which would be like 20% or less of all of them.
Most commonly used incentives that I've encountered are like the one used in Loren @Hammerhands, where the party splits up. Similar solutions have been used, eg, in Aldorlea's Book of Legends, where at the Boss fights, the heroes are attacked from several sides at the same time, and thus the party needs to be balanced out to anything from 2 to 4 different teams. A more creative solution would be something like the one used in Deadly Sin 2, where the melee members of the party storm the tower where no magic can be used and the mages go up the tower where melee attacks are of no use. Another exercise in this happens in Laxius Force III where the characters are divided into groups by the element they represent. If the player chooses, say, an air-aligned character to go into a water cave, the character's HP will be squished and it'll fight really slowly.
So, one way to force people to fight with different combinations, would be to add a storyline
quest, which can be completed only with a group of thieves, and other quests than can be completed only with mages and so on, but not with a combined group. Or there could be a storyline quest that requires eg. speed above certain level. Not that this method is very innovative, it has been done several times before, but in my opinion, it does work. EDIT: Also, one of those weaker, "annoying" characters could have nice money or equipment stealing skills, etc, that would benefit the player if they used the character during fights.
To force using different characters through required rest is an interesting idea. However, I do agree with the comment said here earlier, that on Easy difficulty, a player should be able to lean mainly on their most favourite bunch, at least without too much of a hassle.