Ignoring the potential split for a moment, it would be a smart move for Bitcoin to be merge-minable.  I believe that I've amply demonstrated that mining will always approach being iffy from an economic perspective no matter what the coinbase reward, fees, transaction rate, etc.  Many times it will drop below, and I've heard reports of miners shutting down since they cannot operate in the black at this time.  Same thing happened a few years ago IIRC (though that was probably somewhat associated with the GPU -> ASIC transition as much as a price drop.)

So, Bitcoin's best hope to retain a safe percentage of potential sha256 hashing power is probably to hope that people mine Bitcoin as a side operation in order to pull in some extra bucks.  With a healthy sidechains ecosystem miners would probably be incented to support a given sidechain with a variety of rewards.  I would think that most sidechains would be designed to induce miners (and other support infrastructure like transfer nodes) to also support native Bitcoin since the sidechain relies on a healthy native Bitcoin for it's value proposition against other monetary alternatives.