Chaosmancer
Legend
I think the high-ish DC is because if it was, say, 10, then Rogues with Expertise in Stealth would soon be doing it virtually at-will. DC 10 is likely a 85% chance for a 1st level Rogue with a +3 in Dex and +4 in Stealth. Then they hit Level 5, and now they probably have a +4 in Dex and +6 in Stealth. Already, they'd never fail it.
At DC 15, the 1st level Rogue has a 60% chance of success. Decently high, but with room to grow. Now it's an 75% at Level 5, and doesn't become automatic until Level 9.
I could also see an argument made that the DC benefits the player by reducing variance. A DC of 15 is higher than most monsters' passive Perception. A PC knows that even if they barely make it with a 15, they have a good chance of staying hidden, while with a 14 or lower, they know they failed, and can make alternative plans.
All that said, personally, as DM I think I'm going to stick with enemies' passive Perception as the DC. The new rule is streamlined, and may be easier for new players and DMs to handle, but I have 10 years of experience with 5e, and have had no issues with stealth. Or, at least, I'll ask Rogue players which way they want to go: the clear Yes/No of the 2024 Hide Action, or the more swingy Maybe? of the 2014 Hide rules.
I think it is also important to consider the Rogue's (or other character's) perception of their own roll.
Nobody is ever happy or satisfied with a 10 or 11 on their stealth check. Those sorts of rolls are always followed by grimaces of "well crap, I failed". You don't start getting into more hesitantly okay with it until you hit 13's. 15 is usually where people intuitively feel like they succeeded.
So, setting aside the actual math of success, emotionally, this fits with what people have come to expect from 5e DCs.