So in this case you favor installing and maintaining elastic search? I don't think so. It seems it would come with more than $50/month cost in terms of maintenance and hosting time, as well as the extra hassle.
One thing they all have in common is that they're no longer 2 person shops. When you're at a single digit pre-PMF size, spending time on setting up your infrastructure and tooling is irresponsible. At some point the cost of the SaaS becomes greater than the cost of paying someone to maintain the tool, at which point you can do the switch.
And that point can come very early. We are handling a lot of data/user. We are hosting our ES for ~$80/mo which would cost $650/mo at Algolia for the same volume. Same for logging data. We are hosting our own EHK (Heka instead of Logstash) stack for ~$50/mo (few hours of setup and ~10mins/month of maintenance) which would cost us about $500/mo if we would have stayed with Loggly (and ours will stay at about the same price well into the volume of Loggly's $1k/mo plan).
As a bootstraping startup you don't have the luxury to throw money at problems and a lot of SaaS are not well suited if you have a heavy data workload.
There is also the masters of search: https://www.google.com/work/search/products/gss.html#pricing... but looks like the price goes higher when you have a lot of queries. Also you probably can't customize the query result as neatly as algolia