While the idea per se may not be so terrible, it will requires a complete rework of everything: maps, creeps, Heroes, mercs, objectives and so on.
With a smaller team working on HotS, I really doubt they can ever even consider to remake the whole game and try out such things.
I had this exact same thought. But not 3v3, do 4v4. Straight up 4v4 makes sense.
The lanes account for it, balancing heroes account for it, and it prevents the “5 man pain train” that constantly appears, and is almost necessary for the meta.
Make it a brawl gamemode that can always be accessed from custom. Making it it’s own full blown gamemode would just split the playerbase even more.