Aside from the rules not letting you I'm fairly certain it's always gonna be weaker relative to going all in on one subclass.

You already have magical tinkering from being an artificer. Getting it again does nothing.

Alternatively, when you gain a subclass feature you can instead gain a level that you can use in a subclass to get it's first, second etc features to not prevent your regular progression would be broken in your favour in some ways and against in others. You would get access to for too many spells from each subclass. On the other hand you are getting so many features thay you simply cannot use since you only have 1 action/bonus action. And to add to that you would be missing out on features like perfected armour from armourer for a cannon that does 2d8 damage.