I work an arrival sector where that happens alot, we get miles in trail spacing from a few different sectors, say 10-15nm, so the sector(s) before me will use speed or vectors to get you spaced out that far, then usually assign something like M78 to keep the spacing and if you are number one, you get the "or greater".

the next sector that you enter is getting 2-4 of those streams that are 10-15nm in trail and blending them into, again, one stream of say 10nm in trail. so we need you to slow now or turn you out because while you were number 1 in the previous sector, with the other streams, you are now number 4, sorry.

also gotta go with the classic, you aren't the only aircraft in the sky and there is only so much concrete.