What if all nodes on the lightning network were watchtowers by default? What would be the costs for forcing every node on the lightning network to provide watchtower services by default so that the burden is shared by other users maintaining the default and with consideration for relative value across the second-layer and for the rate at which users go offline? Could this work for lightning or other state channel networks? Why, or why not? ‬

So, what if all nodes in state channels are arbiters/watchtowers by default, but the cost of computation to support watchtower service on the network for a node (or node pair/channels) depends on the cost of ‘need’ of that node to have state/in channel transactions backed up, which is relative in value to other nodes in the network and to the rate at which nodes fail in the network. State channel users may choose to not use watchtower services at all, use watch tower services but not support it for others in the network, in which case they pay watchtowers at a premium, or to both support ‘watching’ and establish state channels. Also, if the responsibility of ‘watching’ should have a reasonable level of redundancy over periods of time so as to relieve the burden of computation costs of all watchers... sorry

tl;dr - the first part up to ‘why or why not’^^;
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.