With single stage shell holders, the height of the shell holder (and the height of the "deck" that the case head sits on) can vary between manufacturers. That can lead to not being able to size a case down enough. And since every die maker has their own shell holder numbering system, having their shell holder keeps you from having to look up "what RCBS shell holder is the equivalent of a Hornady #16?"
On a progressive, there is a similar situation, but fortunately both Dillon and Hornady progressive shell plates seem to have plenty of clearance. Instead, the bigger progressive problem is die length; can you adjust the die down far enough, given the height and thickness of the toolhead and deck?
I think that, as long as you use a consistent shell holder with a particular set of dies - and if you are able to get sufficient sizing with that setup, then you're fine. But while I have not always followed this advice, I'm working on correcting it for my own dies. I "went cheap" with a lot of dies and didn't bother to get the shell holder when I bought the dies because I had a shell holder that would work for the new caliber.
That's a big mistake if you have more than a couple sets of dies. Where's that shell holder? Did I leave it in the .223 box, or the 380 Auto box, or maybe the 300 Blackout box? I have that issue, but with a number of different shell holders...
So
at least get one shell holder for each set of dies, and
preferably the die maker's shell holder. It sure helps to decrease confusion, saves time searching for that darned shell holder, and since they're $5-$7 each, it's really cheap to keep up with. Unless you're catching up, like me.