New full-backs should help massively, for sure. Still, I think an attack where none of the forwards can really offer penetration through dribbling might not be the best idea. Every top attack should have someone like that imo. Barca have Messi and Dembele, City have Sterling and Sane, Real have Ronaldo (less so these days), Isco and Bale, Juve have Costa and Dybala, Bayern have Robben and Ribery, PSG have Neymar and Mbappe, Chelsea have Hazard, etc. All players that are/were capable of beating one or two men on their own and stretching the play when needed. I figured that it would be Sanchez for us, but he barely tries to beat his man lately and seems to have slowed down. I'll wait until next season to decide whether it's a decline or just fatigue though.
Different level of player obviously, but I remember a game (might have been West Ham away) where we paired Sanchez with Mata as the wide attackers and they spent most of their time passing it about in the middle because they couldn't get past their marker. On the counter, they'd probably be great, but we'll be on the front foot in a lot of games against a low block, which is where we might see problems every now and then.
Let me make it clear that I'm not saying Griezmann would be a disaster here. It could work out, but, unless we go back to a 4231, I don't feel he's the ideal option for us as some are saying.