Is there anywhere in this series where having a thief character (either single or multi-classed) in the party is absolutely necessary?

You can beat the series without a thief in your party but there's a big optional challenge in Death Knights where "A party without a thief will have difficulty surviving." according to the cluebook and there are also a few options you can't take during the games.

I recommend a tripleclass Qualinesti fighter/red mage/thief if you want to have as little thief as possible, maybe a kender cleric/thief in the first game replaced by the tripleclass in the second.

Thanks for the info.

I'd say the Kender is most useful in the second game, due to the Skeletal Warriors, but the elf is more useful in the last game.

Usually the games will give you a NPC if one would be useful. I always make one anyway. A kender cleric/thief is basically only good for yelling, hold person, and turning undead, but that's not exactly useless.

Characters at the end of the 2nd game have far more XP than freshly created ones in the 3rd so it's better to switch after the first game.
Characters freshly created for the second game will start at about the same level as imported ones and triple classes will even have more HP than you can get with reloading.

Yeah, it's hard in a practical sense not to include a Thief, because pretty much everyone goes for a Kender, and a Cleric/Thief is the only really viable high level class setup for Dark Queen (Cleric alone caps out in Death Knights and Fighter and Ranger have pathetically low level limits).

As for whether you actually NEED a thief, I've only heard of one bit of quest-affecting content that seems to: if you want to help out the rebels completely in New Aurim in Dark Queen, you apparently need one to open the city jail locks (I've seen at least one walkthrough writer note that he was unable to open them with Knock, nor with 23 Strength).

Dave's Challenge should be able to be completed without a thief but you probably do want one there or you'll take a lot of unnecessary damage (and resting is a pain there, pretty much need to save before each time you do it); even the exit door if you just want to back out is trapped (which kinda raises the question as to how you got inside in the first place but ... whatever ...).

Not that there's much reason to avoid taking Thieves anyway, especially with how useful the back stab tactic can be (particularly with so many of the boss tier enemies being 1x1) and the fact that multiclassing is a lot more favourable here than in the Forgotten Realms games :)

Of note, from what I have read, in DKQ, a Kender Thief/Cleric can use 6th and (if neutral) 7th level spells, meaning that character can be a functional healer.

Unfortunately, when making DQQ, they decided that characters with 16 or less Wisdom can't use 6th or 7th level cleric spells, making such characters useless as healers (let's face it, Heal is the only viable healing option other than resting at high levels, unless you purposefully kill and cast Resurrection on a (non-elf) character), and Kender are limited to 16 Wisdom. (Of course, you could get around that by hex-editing the save file and raising your Kender's wisdom, but most would consider that cheating.)

I thought they implemented that for Death Knights of Krynn as well - at least according to the manual. Guess I'm gonna find out (although my party has three clerics + a knight so no biggie).

As for thieves - one of my favorite parties was made up of multiclassed thieves save for one human knight. Had a blast just backstabbing everything:

Human Knight
Hill Dwarf Fighter/Thief
Hill Dwarf Fighter/Thief
Kender Cleric of Majere/Thief
Qualinesti Elf White Mage/Thief
Qualinesti Elf Red Mage/Thief