Why does this matter? If they can provide 99% uptime for the service they provide, I don't care.
> What the benefit to using Nekoweb over publishing static content to S3/CloudFront?
This is the attitude that kills the net. Sends of the vibe "It's not on AWS so it must not be used, don't you dare".
What the benefit of to using S3/CloudFront?
I suppose it all boils down to that folk not knowing the old internet. The understanding where you relied on hosting companies to provide webspace with an banner, or paid-so webspace that's now lost in today "innovative" world.
One day the clouds will fall, and your site will be with it.
CloudFlare has been losing money for ages. I use it but seemingly everyone is sure it'll last forever.
With static, if it dies tomorrow you take the raw html files and move it elsewhere. Sure, it's an inconvenience, but it's the same as to why you don't use a second hand eBay server for commercial piece of kit. I learnt that the hard-way.
...what?
S3 launched in '06 and is coming up on 20 years of being a thing. At this point it's had a stronger/longer lifespan - and will likely continue to do so - than pretty much any of the old net hosting sites.
OP was clearly just asking why bother using something like this over <insert your choice of host here>. The only real answer is that you want to do something different - and that's totally fine.
Many providers nowadays have existed long before S3, 1&1 (now know as ionos) are another.
So? My server has had just four years uptime that's not including all my other servers I've been hosting since the age of 13. I can service exactly the same as to what S3 can do. I just don't have £LOL fund where I can invest in providing back-end infrastructure like the corp can do.
I foresee it to likely continue to do so in to the future, I even have strategy plans for it when I pass away.
And I doubt the type of user Nekoweb (and Neocities) targets is well-versed or comfortable with S3/Cloudfront.