The first plane I bought, secondhand, was concave. It took me a long time to realize. By then, I had bought a new no 4 Stanley. This was badly warped. I had both surface ground and I estimate the latter was at least 1/8” out of square. This didn’t cost very much. But, pardon me, if you have ever struggled to use a plane, it may well be because the mouth is either higher or lower than the ends. Since the post above, I have flatted two more planes, one convex and the other with high spots here and there.. I remembered an off cut of granite worktop and stuck 80 grit abrasive, and that I found was rather quicker, although it might have resulted in uneven ends.. But if the plane is concave, you would have the blade projecting too far, it will chatter and the shavings will jam the mouth, it won’t be a comfortable ride and the surface of the wood may look as if it’s been adzed!