I don't know about the immediate financial impact, but generally speaking it's always better to take a shot at getting a contributor on a cheap 4 year deal. Anyone they take with such a late pick wouldn't cost much either, as opposed to someone like Brown or Taytum who are making 7 million just based on being 3rd overall picks.
But yeah, just generally if you miss a draft there's a gap in your team building. It's hard to fill gaps every year by hitting perfectly on cheap signings like Baynes, Theis, and Larkin. More often the talent available for those bargain prices, well, is hard to refer to as "talent" in the first place.
Unless you overpay, it's hard to get the vet role players you need for a contending team on long-term cheapo deals, which is why the Crowder deal was such an amazing steal while he was playing so well. The task of re-filling those spots because guys get too expensive (see: Baynes this offseason) is difficult, so if you somehow hit on a young player who is guaranteed to be around for four years it's a real boon.
If they keep Rozier for next year, he'll be providing unbelievable 2nd unit/6th man depth for pennies. He's doing 100x more than what a typical cheapo free agent vet signing would usually do, and he's also very tradeable to teams that have trouble attracting FAs or want to get a leg-up on maybe signing him next year.
The draft picks are basically like lottery tickets but with odds that improve based on how good your scouting is. If they hit, they're more valuable during those four years than anyone other than the top stars, both as a cheap rotation player and their value as trade bait.