I don't disagree with your logic; a sleeve lets the welder turn up the heat enough to get full penetration while minimizing blow-through, and with higher heat there's no need to chamfer the edges (by chamfering I meant basically breaking the sharp edges down, since the wall thickness is less than a millimeter).

I have indeed made internal sleeves to butt-weld thick-walled aluminum tubing (for the lock bars on my cargo trailer). One hassle to making internal sleeves is that the outer diameter (OD) of the sleeve must match the ID of the tubing, ideally it would be a tight locational fit. I have a lathe so it wasn't a big deal to turn the sleeves to the right size, but I don't know if the OP has that option available. So my thought was to eliminate the sleeves and have the welder, assuming he/she is skilled, turn the heat way down while still achieving a full penetration weld. Easier said than done.

Which ultimately brings me to my (revised) conclusion: Whether using an internal sleeve, or butt-welding without an internal sleeve, this in all probability will look like a kludged repair job. The weld must achieve full penetration all the way around, since any nonconformities will introduce stress risers and possibly begin cracking. Plus, when the weld is complete, it won't be a perfectly flat surface all the way around. Best case, it's a convex ridge all around that can be carefully ground and sanded flat and smooth. That's a whole lot of work and very tedious. Worst case, there's undercutting (depressions and incomplete filling) at places in addition to the raised ridge. The undercutting will require filling with body filler before painting. Undercutting also introduces stress risers and since the material is thinner there, the frame may fail.

So while the frame could be repaired by cutting out a bad section in the middle and butt-welding a new piece in, IMHO it's not a great solution, at least not for a frame that supposedly is worth a lot of money. My thought now is that the best solution is the earlier suggestion of cutting the tube out entirely and replacing the whole piece. Grinding the old welds off won't be much more work (if any) than trying to grind new butt welds perfectly smooth. Now there would be a smooth new tube, with no stress issues.