One of 5e's "features" that is supposed to be a strong point is not spending much effort on RAW in favor of forcing the GM to finish the system on the fly.
It's definitely a feature, not a bug. 3x had too many rules that bogged everything down. It's not "lax," its there to prevent unnecessary over-tuning. Plus, the more rules you have, the easier it is to mess something up by accidentally breaking it.
(And I say this as an autistic person who
really likes to have her rules written out plainly.)
I've never seen wotc weigh in on if paladin is supposed to be able to multi-divineSmite in one turn or not
From the paladin description:
"Starting at 2nd level, when you hit a creature with a melee weapon attack, you can expend one spell slot to deal radiant damage to the target, in addition to the weapon's damage." Compare to the rogue's description of sneak attack:
"Once per turn, you can deal an extra 1d6 damage to one creature you hit with an attack if you have advantage on the attack roll." So it's pretty clear in saying that you're
not limited to one smite a turn. Paladins can nova the hell out of a target if they want to and have the slots to do so. Rogues... can't.
Also,
smite spells are different than the Divine Smite special ability, as evidenced by the fact that non-paladins can take the spells (e.g., a Hexblade can take
wrathful smite) but can't Divine Smite, any more than a warlock could Lay On Hands. Your paladin wants to cast
searing smite and then you decide to Divine Smite on top of it? Go for it! Bring down the wrath of your oath upon your foes!
The warlock thing is a bit vague, I admit,
but warlocks aren't technically "real" spellcasters (Pact Magic is it's own thing; if you read the "Spell Slots" section under multiclassing, you'll notice that warlocks aren't included). So what this means is that a multiclassed warlock gains only its warlock spell slots after a short rest, not all of its spell slots.
If you don't enjoy houseruling, I can see where you would be frustrated. But in the long run, it's pretty simple: go by what the actual rule says paladin entry
doesn't say 1/turn, so it's not 1/turn), and don't worry about how it intersects with another rule until that situation actually comes up in play
and causes a problem. There's no real reason to fix something that hasn't been proven to be broken.