I think the problem sits more on monster design rather than PC build.
Magic resistance is too generic/generalized and too common.
Legendary Resistance is a very potent ability, undervalued in design and broadly applied.
It would be better to make monsters resistant on certain saving throws (wisdom or charm) for example.
Legendary Resistance is the same as immunity unless you have multiple spell casters.
Even then, legendary resistance is just a tax on your spell slots.
Couple that with the fact such creatures have high saves to begin with. Even with multiple casters, burning through legendary resistance is next to impossible and often a waste of spell slots.
We have three casters in our group. Cleric, Bard, and Wizard evoker. We have yet to burn through Legendary Resistance. In battle, we have other things to do than try to launch a spell every round that tries to force the creature to use Legendary Resistance. Buffing is big. Healing for the cleric is big. If concentration breaks due to damage from a big breath weapon or AoE attack or if one of us goes down to damage, we have to buff the character again. Lots of stuff going.
People that think in a big battle you can launch save spell after save spell at the Legendary Creature are theory crafting. You can't actually do that. You have other stuff going on and other responsibilities. You are getting hit by Legendary Action attacks and Lair action attacks which can disrupt Concentration making it so you must cast buffs again. You don't have time to see if you can burn Legendary Resistance down. By that time your martials might be dead or you might be dead. You have to be effective. That requires using attack roll spells that guarantee you do some damage. You can't be wasting time hoping it misses a key save.
It's all been very different in actual play than I thought it would be. A few random lucky rolls change everything in a fight for a monster. A random lucky save and you wasted not only a precious spell slot, but an action and an entire turn that he monster uses to rip you apart. The creatures with lair and legendary actions are dishing a lot of damage very quickly. You have to do the same or you're going to die.