To use arbitrary numbers, let's say the XP for a 4th level creature is 4x the XP for a 1st level creature. In order for it to be an appropriate challenge, then having 4x the hitpoints is about right. Having the same attack bonus, in bounded accuracy, is about right, as is having the same defence. Having 4x damage is.. wrong.. because in fact the correct scaling is 4x the attacks with the same damage. Obviously that isn't going to swing (an extra attack every level is madness) so this scaling is wrong.
If you had the same number of monsters vs the same party using the same attacks, then a monster with 4x the hps is going to stick around 4x as long, and thus get 4x as many attacks, so that bit actually works fine. But, faced with a 'big bad,' the party just might pull out some bigger attacks or some action-denial, and then the quadruple monster folds.
It's a monster-design lesson that was learned during 4e, the original solos failing to be quite the threat they were meant to be for lack of action-preservation.
What scaling do we use? I've agonised over this and not found an answer because encounters with different numbers of actions are so hard to compare. If PCs and creatures grow in power linearly (a hit dice, a damage dice per level) then combats remain the same at every level.
It remains similar in length, sure, and comparable in encounter balance. If characters also gain more options and monsters gain more dramatic abilities, though, the feel of the combat will change. There can be more to 'scaling' than the literal, bigger-numbers, side.
If they gain hit die but do less damage then combats start to last longer. This might just about make up for the lack of actions for individual creatures. That's the only way I can see it working - damage output scales at, say, the square root of HP increase. Combats get longer as you go up in level.
So, not less damage, but lower increases to damage than to hps? I could see that working in some ways: it'll give PCs more staying power as they level, and make overleveled fights longer (and, thus, perhaps, more dramatic, if they don't become 'grinds').
But it still doesn't quite let monsters pull double-duty as solo threat vs a lower level party and mook vs a higher level one. The effect of automatic focus-fire, on a lone monster, by itself, changes things. Then there's the impact of action-denial.
Maybe there could be some sort of advantage given to the much higher-level side of a battle to both put back a little of the spice/drama that bounded accuracy might take away, and to speed up underleveled mook combats and add danger to overleveled boss encounters? Not Advantage in the 5e jargon sense, of course, blanket advantage/disadvantage could get pretty boring, but some other mechanic. For instance, in AD&D, a fighter got lots of extra attacks vs less-than-one-HD monsters - 1 per level, in fact - and AD&D dragons had a fear aura that only worked on creatures below a certain level/HD. Since 5e is all about poking around the attic for such ideas, why not do something like that? A Fighter could, say, trade in a CS die for an extra attack if all the opponents he attacks that round are below a certain max-hp threshold - there's already a cleave-like option under one Fighting-style, but this would be a blanket thing, like Parry. Casters, of course, can already sweep away hordes of lesser monsters with area attacks. A monster could gain extra 'secondary' attacks or have additional combat options that it can only use, if it's level/HD is sufficiently higher than the party's (or everyone in the party is below a certain max hp threshold, since that seems to be 5e's implementation).
