I've got a Titan XP (2016) and I had it on the stock cooler for a while. I also had a 1080 and a 980 on the stock coolers before swapping them out with the Acellero Xtreme coolers.
I've got an Acellero Xtreme IV on the Titan P at the moment and I've actually got one of the closed loop Kraken kits from here in the recent sale. Will be interesting to see how much it improves things! Even with an Acellero Xtreme IV, it can still end up at like 80 degrees!
Regarding the stock cooler, I would say if you can be bothered to change the cooler, do it. You'll be a lot happier in the long run and won't have the stock cooler driving you insane. If you're going to do this, however, keep in mind that until you've done it a few times installing the Acellero coolers can be a nightmare (make sure you get the correct hex keys to remove the stock cooler!!!!!!!!) and you might be bashing your head against the wall for a couple of hours before you figure it out.
If you're going to stick with the stock cooler, I would say take the power limit down a little. Even 5-10% won't cut off much performance, but will cut out a lot of noise. Either that or simply manually set the fan to what you can deal with (which is usually 60-70% depending on the game for me) and then the temp will be what it will be.
I would also look into 'undervolting', which as far as I'm aware on the 10 series cards can be done by using MSI afterburner to force the card to sit at a specific voltage with a specific boost clock (as long as it stays within the power limit). If you can't find any information on this, I can see what I can dig up.
Personally, I was kind of okay with the stock cooler on the 980 and 1080 (low TDP cards), but I got rid of it as quick as possible for the Titan. IMO it just can't deal with the higher TDP on the 1080ti/Titan cards very well