Could work, but would need a few special rules.
-Dieing drops the flag, after 3 seconds of not being picked up by another enemy, it is automaticallty returned to its base.
-Teleport is disabled.
-Carrying a flag makes you visible, and marks your location on the minimap. (Sorry
)
-You can not use abilities, summoner spells, or items while carrying the flag, and you become unaffected by those used by Allies (So your allied Ryze can't just warp you out, Tahm can't eat you and speed away, you can't Shen ult to an ally at your own base, etc. etc. etc.). The Flagholder buff would grant defensive stats though, so you don't just get murdered in 1 shot all the time. You have to protect the Flagholder and escort them out
-Since it's basically a 4v5 when your ally has the enemy flag, there needs to be something to offset this. A global teambuff that grants CDR and some other stats to help (thought of raising CDR cap also exists as part of the buff).
I think the game mode would be interesting, and could definately work out once some basic balance rules (like above) are worked out and tuned.