You're actually right, and I'm surprised it doesn't get mentioned more. Sterling may line up on paper as a winger but he tends to play very narrow. As you rightly point out his delivery from wide isn't the greatest either, so in a lot of ways his actual role is more like a 2nd striker.
But this leads me to what I feel is a significant "problem" with the team and the reason I thought Zaha was worth a look over Mahrez even though Mahrez is in my opinion the better player.
We have a wealth of players who can deliver a killer final ball from the left because they are excellent left footers on the ball. Sane, Mendy, Zinchenko and now Mahrez can all deliver a killer ball from the left into the box. Even Silva can deliver a killer cross. On the right, both Sterling and Walker are relatively poor crossers (walker is arguably our poorest player on the ball period) and Danilo who I would say is better but still doesn't have the greatest final ball. This puts a lot of pressure on Debruyne to provide our delivery on the right. Debruyne was amongst the top crossers in the whole premier league and it's because he is really our only right footed player who can reliably deliver a good final ball from wide right. However, when he is doing that it takes his genius away from the middle of the park.
In most games it won't be an issue because we'll generally be too strong overall anyway. But we got found out a few times on this last season. In particular our away game in the league against Liverpool where Liverpool identified that our right hand side didn't provide as much threat and that we we were basically sending everything dangerous through Sane on the left. I feel our attack is very lopsided and adding Mahrez has only made that problem worse. We have a bunch of players who like cutting in narrow on the right or delivering from wide on the left but noone highly capable of delivering the ball consistently from wide on the right. It reduces our options and can leave us vulnerable to being shut down on the left.
I had hoped we would sign Zaha instead of Mahrez (despite Mahrez being the better player, I felt Zaha bought better balance to the team) or a really effective attacking right back like João Cancelo (who ended up at Juve). Maybe Danilo will step up this season, I do think he is underrated and we haven't seen the best of him yet. Maybe Sterling won't sign his contract next season and we'll sign a Zaha or similar who does have top notch delivery with their right foot. But I do think the lop-sided nature of our attacking options is our biggest weakness going forward right nownand a savvy team, particularly in the champs league can suss that out.