Characters don't have dual roles.
Would it make sense to have character X summon himself from an Assist Trophy? No, it wouldn't.
There's a reason why Toon Link is replaced by Alfonzo on the Spirit Train. There's a reason why Charizard and Little Mac stopped being summons when they became playable.
The only exception for multiple characters is multiple players selecting the same character, also being forced to use a different color/alt. This is obviously due to gameplay, as it allows any player to pick any character. Would be unfair otherwise.
An exception does not a rule make.
You lost me the second you tried to tie "Making sense" into Smash Bros. Doesn't make sense that we can have Sheik, ZSS, Samus, and Zelda all in one battle, or 8 of any character for that matter, yet it happens anyway.
Yes, there is a reason why Charizard and Little Mac stopped being summons. They were planned that way from the get go, there is no point in adding in an AT of a playable character. Promoting an assist to a character, however, has a point, it brings further attention to the character, allows the developers to do more things with the character.
You can have a Riki AT on the field and have him summoned in Shulk's Final Smash at the same time. This doesn't cause some sort of Smash Bros apocalypse. If you happen to pick the same character and color in Online mode the game doesn't force one person to switch colors.
An exception does not a rule make, yes, but there isn't an official rule there in the first place!
Sakurai wouldn't just go through all the time and trouble he would need to convert an assist trophy to a playable character.
Instead going through the trouble to build an entirely new character from the ground up?
If somebody can give me a source as to why the development team is incapable of making an AT into a character and removing/altering/doing nothing to the original AT, i will wholeheartedly agree with you that this will never happen and drop the entire discussion. But this is a possible scenario that could happen. Suppose a reboot to Murasame Castle comes along, something that was not planned when Takamaru was decided as an AT. Assuming DLC continues, is it so improbable that Sakurai would hear about this, look at Takamaru's role in Smash Bros, and decide that he could be upgraded? If you can answer that with a no, then please tell me what other characters might be coming as DLC, because you clearly have some sort of inside look into the Smash development team that the rest of us do not.
EDIT: I would also like to point out that dual roles are all over the place in Smash Bros. For example, you can have the Pacman Ghost AT's on PacLand, where the Ghosts are also a stage hazard, and have 4 different Pacman's on the stage also summoning ghosts through his moveset.