LOL!  I like it!

Actually, one of my rationals for keeping Bitcoin lite and tight is that I could see users getting a significant break on some sidchain implementations if they supported the Bitcoin network as something of a tag-along even if they never needed to use it natively.

Even if sidechains are lazy and will let others do the work of securing the backing store (which must be assumed for design purposes) I could imagine sidechains themselves needing to compete with one another to exercise their pegging operations against the mainchain in a timely manner.  If their own userbase were supporting Bitcoin this could give them an extra advantage over simply paying reasonable fees.

I'll mention again that in efficient sidechain implementations, a single backing store adjustment (Bitcoin transaction) might reflect many thousands of underlying user-level transactions.  Thus, users really could pay a trivial fee.  The economics of native Bitcoin support are then equivalent as a low-use backing store and a high use 'one-size-fits-all' scenario it just that the risk of centralization is just about the opposite.  Indeed, various sidechains can target different (and sometimes mutually exclusive) market segments so mass utilization rates could be much higher (along with the reward for supporting native Bitcoin of course.)