I personally think it was a great idea, but executed poorly.
The mode is way too chaotic and you have nearly no control over the outcome. Making strategies is impossible because everything is constantly changing, and it's impossible to adapt.
But what absolutely killed the mode for me, was having the final battle have a time limit, as well as using the scoring system in time. It simply would have worked far better as simply a stock battle using the team you managed to build up.
What would I do to improve it?
First off, I'd make it so that each player has a turn separately. Having every player use an item at once and then all moving at the same time simply takes away any sort of strategy away from the game. Sure, randomness is good in these kind of games, but Smash Tour takes it too far to the point it puts Mario Party to shame.
Battles? Honestly, only the players that are actually in the same space should participate. It would make it feel more personal, and there'd be an actual reason to avoid or chase other players.
Something that should also really be possible is the ability to actually choose the character you want to use from the ones you have collected. If I have three different characters on my list, I shouldn't be forced to use a specific one in the next fight. Let me use the one I like the best, or the one I'd rather not lose. And talking about fighters, each one simply feels like a random button now, they're constantly rotating due to fights and items, and it's impossible to preserve one you like. How about making it so that the only way to lose a character is by losing a fight? Doing that coupled with the ability to choose from your list before each battle, as well as perhaps choosing the fighters you start with, would make the whole thing feel like you're customizing a specialized team of your own rather than collecting a bunch of random slots.
Also, this isn't necesarily needed for the game to work, but just imagine it.
Remember the games in Smash Run? There was a Race to the Finish, a jumping event, a game where you had to defeat the most monsters... How about implementing the same mini-games in this thing? After each round of turns, a minigame could be selected at random (much like in Mario Party) as well as some other possible fun stuff, like a Multi-Man Smash, or a competitive Home-Run Contest. All players would have to play, winners are rewarded, losers lose a fighter. It would also be separate from plain battles, each turn you get a mini-game that's not a Smash fight, but if two or more players end up in the same space, they fight for eachother's characters. Doing this might make the whole thing a bit too similar to Mario Party on a basic level, but the whole thing about collecting fighters and ending it on one big battle with the team you have been building throughout the game would have made it more than different enough to be worth it.
And that is why I dislike this mode. It was simply a massive waste of potential. It could have been so much more with only a few rule adjustments, but we instead got a huge mess of chaos that completely lacks direction.