What if all nodes on the lightning network were watchtowers by default?
Not sure if I get exactly what you are asking for. But some general remarks and thoughts should hopefully give you all the information you need to answer your question.

A watchtower basically needs  a copy of your channels state history. (a subset of the data will be sufficient but let's assume for simplicity that the watchtower needs an exact copy of the history of channel states) 

Now the answer to your question depends.

If every watchtower is supposed to have the full history of every state channel on the network we would have a total storage requirement of O(V*E) with V being the number of nodes on the network and E the number of channels. And a single storage requirement of O(E). Unless the person is a supporter of some Bitcoin forks like bcash, one can easily see that this would never scale as the number grows linear with the amount of payments taking place in the lightning network. This it has a storage requirement in the same order of magnitude as storing all transactions in one public blockchain with really large blocks.

However we could say that it is sufficient for every node to be a watchtower of x other nodes. In this way on average (amortized) every lightning node should have a storage overhead of a factor x with comparison to the storage requirements for their own state channels.