Why pay a fee to have your article (in a subscription-based journal) made open access when you can just put the preprint on arXiv? Upon acceptance, some journals offer open access through an optional fee. This model differs from the usual open access model in which all authors pay a fee and all accepted papers are accessible without restriction. Addendum: the latter is referred to as simply open access, while the former is referred to as hybrid open access.

My question is as follows: I publish (most of) my papers on the arXiv, and as such, the preprints are picked up by search engines. When the corresponding camera-ready journal version appears, anyone with an internet connection can still access my arXiv paper, and hence I always opt not to pay the optional fees to make my paper open access.

In fact, most respected researchers in mathematics/computer science/physics/etc. also publish to the arXiv. As such, I am confused as to why this model of open access exists. What demand is it satisfying? Is there some advantage to paying these optional fees that I am not seeing?

P.S. -- The journal I have in mind currently is a SIAM journal. Their open access policies are listed here. Their open access fee is $2,500 USD (this is not an unusual number for publishers following this approach). This (at least to me) is a substantial amount of money per paper.
If you work in a field in which people use and trust the arXiv, then there's little reason to pay fees for hybrid open access.  One reason would be if your funding agency requires open access publication and does not consider the arXiv to be an acceptable substitute.  Another would be if you wish to encourage the journal to transition to fee-based open access publishing.  In your case, I doubt either of these reasons would be compelling.

From the publisher's perspective, it's a no brainer: why not offer authors this option?  It can't do any harm, since it pays for itself.  If few authors choose to pay the fee, then the publisher can use this as evidence that there is little demand to change their business model.  If many authors do, then it smoothens the transition to becoming a fully open-access journal.