+1 for the SteelSeries Nimbus. Had one for a few years now and it’s excellent. Great battery life, charges via Lightning, and pairs really easily with a variety of devices.
The only downside for me is there’s no equivalent of a select button, which can really hinder you on certain games. Not so much on iOS as the control schemes for those games are usually a bit more simplified. But I also use it to play games in OpenEmu on my Mac, and the lack of select button is a dealbreaker for games like Metal Gear Solid.
So while it can’t be the one controller to rule them all, I think the Nimbus is still the best all around controller, especially for iOS/tvOS.