How can you distort text without perspective effects?

Object >> envelope distort  >> make with top object could have been the ideal solution. But as you see from my result below is even much worse. Adobe made an effort to address this with Object >> Envelope Distort >> Make with Mesh, but this has been problematic for over a decade on type distortions or similar strong linear edges. Playing with the mesh handles is time consuming back and forth, but once in a blue moon and get you an acceptable result

After many years of using Illustrator, I find making near perfect type distortions to require much time in manual adjusting to get an acceptable result. So my estimates are high when I need to do this for final art.

There used to be a photographic method  up until late 80s using distortion wheels that could do this. While that also involved a dark room with a large wheel and film/chemicals andmultiple attempts, I felt I could get a better result.

You can use the bottommost option in the free distort panel or with modifier keys: https://helpx.adobe.com/illustrator/using/scaling-shearing-distorting-objects.html