In theory this could lead to problematic investments being made, since no individual robot would know what the others are doing. For instance, one robot might decide to sell a certain stock or fund for tax loss harvesting purposes, but a different robot might buy the fund the next day for its own reasons. This would count as a wash sale and would affect your tax liability, but neither robot would be aware of it, so they probably wouldn't notify you of it correctly, so you might not pay the correct tax, which would clearly be bad.
Similar problems could arise, for instance, if the different robots have different rebalancing strategies, leading to an overall allocation that isn't optimal.
In general the idea of these services is that the robots do complicated things that can save you (or make you) money, and they hide this complexity from you. Without knowing exactly what they're doing, it's difficult to ensure that the aggregate action of multiple robots would still be beneficial; they could be canceling each other out, or worse.