So to describe it a bit, I'd say that if you wanted to call down the reinforcements in 4e, you had to go a beyond the game's assumptions.
Not really. Maybe go beyond your assumptions about the game's assumptions. ;P
'Waves' were a definite option in encounter design, one published modules were known to use. They most often involved minions (the sorts of guards and other mooks you'd have scattered all over the dungeon, only to converge when there was trouble), but could be anything. Heck, the very first 4e adventure, sucky though it was (and it was every bit as bad as HotDQ), had several encounters like that.
You'd have to answer questions like "when do I get my encounter power back?"
When you took a short rest, like always. "When do powers that last the whole encounter end?" was a slightly less unambiguous question, and the answer was
after 5 minutes. So, generally, either you got in a short rest & recharged your encounter powers, or any whole-encounter effects you put up were still running.
you had clear XP totals to adhere to for a "balanced" encounter
Guidelines, yes, and they did work pretty well. But you didn't need to 'adhere' to them, they were guidelines, not rules.
even stretched over multiple sites and monsters, something within the XP budget was still "one encounter" (even if it was staggered or something) as far as resource management was concerned.
Naturally. If you had an encounter that could bring in waves, you'd want to consider the possibility of all the waves coming in. If you were running 'tailored' encounters, you could budget it as an 'easy,' under-level encounter, with a worst-case scenario that went well over-level. If you were running 'status-quo,' you didn't even do that, you created & populated the area, and the guideline just gave you a good idea whether the party could handle it or not. You could also pull cute things like interspersing group skill checks to avoid attracting another wave, or run the whole thing as a challenge, with each wave coming on a failure...
In 3e, it was probably worse, because the swinginess meant that going beyond the "one big baddie" model might be a cakewalk or it might be a TPK in the making.
Only in the sense that the guidelines were blurrier and less dependable. You could still either try to stay within them when designing an encounter, or just place monsters based on the setting & situation and use the guidelines to get a rough idea of how challenging they'd be. Same with 5e. Same with any set of encounter-building guidelines, really, the only difference being how relatively applicable, difficult to use, and dependable they were.
Encounter-design guidelines are just a tool. Having a more dependable, easier-to-use tool may mean you don't throw it across the room as often, but you're never forced to use it.
By the same token, in 5e, you can always use the encounter design system, even if it doesn't always deliver the exact challenge in practice that it might indicate in theory. Waves, for instance, while they pile up the degree of challenge much like a single encounter, don't benefit as much from the impact of numeric superiority under Bounded Accuracy, so, if you can be confident that wave 1 will be wiped out before wave 3 arrives, there's no need to apply the multiplier for the total of all 3 waves...
How do you "slam them prone" without some significant investment?
The same way you grabbed them in the first place: by blowing an attack on it. Anyone can do it. Of course you haven't "taken them out of the fight" remotely, but if they want to get away they have to waste an action escaping and 10' of movement standing up, so it's as close as you get to being 'sticky' in 5e, you just give up two attacks to do it.
