This is precisely the range where supercaps shine: time constants of seconds.
Batteries are probably cheaper, smaller even, despite not being suited to such short durations -- probably just because they're a bigger commodity. So, you never(?) see supercaps here.
Batteries are fine: it works just like electrolytic bypass of a much faster example, a switching supply. A 10mJ electrolytic won't handle a 10us switching cycle, it'll have far too much ESR to do the job, or to do it without overheating. But 1J together will.
Likewise, a 1kJ lead-acid won't handle a 1s dropout, but 100kJ together will. As a bonus, it'll keep you propped up for minutes, not just seconds, on the off chance that you need such.
To put it another way: you're fundamentally worsening one performance metric of your system: support time. What are you getting in return for that? You aren't gaining efficiency, because this isn't one of those places where you only need what you use -- while that would be soothing to the OCD,
the real need is availability, and if you aren't saving money or space on supercaps, why bother?
Now, if you're getting these drops so frequently that they're doing substantial damage to a battery that therefore needs frequent replacement, then you've got such a motivation: reliability. You might still want to ask if it's worthwhile to sacrifice the support time by going to supercaps, versus just getting a bigger battery (that therefore can handle the surge demand better -- again, short time demands get distributed better and better over larger reservoirs). Or getting a different chemistry, like a LiPo or LiFeP that can handle the demand with better life.
So, yeah, fundamentally, you're right in the sweet spot for supercaps.
I just wonder if that's a sufficient cause, though, or if there may be other considerations that make you think, "oh, well, I suppose... oh well".
Tim