What front derailleur are you using?

Here is an analysis I did a while ago of an old Alivio triple derailleur.



The problem with the derailleur cage shape was that it was bent outward, and tended to trap the chain preventing it from climbing to the upper sprocket, rather than pushing it over onto the sprocket.

Shifting was improved by moving the derailleur so that it was mounted very high, and avoided using that slanted section of the cage.

A bent derailleur cage could have the same effect.

Everything was fairly worn on that bike. A new chain might have helped.

I do have one bike that shifts poorly to the outer ring (flat). The derailleur barely has enough throw, so adjusting it a bit wider would help. Maybe a different derailleur sometime.

On another bike with flat rings, I think the shifting was worse years ago, but the rings are now so worn that they look like they have natural shift ramps, plus a few rounded teeth. There is also a slight bend behind the crank arms which may also help with shifting (or over-shifting).