My little app Coach Aide (https://soccer.coachaide.com) is a 100% PWA and I wrote the original version just so I can experiment with Progressive Web App (PWA) spec. It's grown to be a pretty useful tool for me and others in youth soccer coaching and I've kept adding features to it whenever time allows (as a sidenote, do not get into sports for business reasons - you think the numbers are big but there's no money in youth coaching and there are only so many professional teams you can go after).
So, obviously being an engineer and writing a tool primarily for myself, I haven't been too interested in promoting the tool to a larger market or making a concentrated effort in increasing its visibility. I figured I let it grow on its own if it deserves so. One of the things I did do though, was to implement a wrapper app (https://stackoverflow.com/questions/53957547/is-there-a-way-to-submit-a-reactjs-pwa-on-google-play/54018830#54018830) so I can upload it to Google Play Store. While I deployed the initial version more than 6 months ago, it didn't really get any installs until in the Fall. By the end of the year though, it had moved to top 10 soccer apps (if you search by "Soccer Tactic Board") but more than 90% of the downloads happened in just the last two months as the app crossed over 500+ installs last month.
So, a few things to note. First of all, the numbers are still ridiculously small. A few of my friends are in gaming industry, and for a comparison's sake, one of my buddy's game gets about 2,000 installs per week - he has several others, yet he is still barely making any money. It's a brutal industry. If people installed Coach Aide at the same install rate, I'd saturate the whole soccer coaching market in the US in a little over two years (http://rapidsyouthsoccer.org/us-youth-soccer-player-statistics/). At the same time, if you have a utility app, it's relatively easy to compete because you are only competing in a fairly narrow segment, as opposed to games that need to take on hundreds of new games released every day on top of the existing game apps. However, for an utility, even with a few hundred competing apps, it's not that difficult to get to top-10 in the segment if you do at least a half-decent job with the app (most apps on the Play Store are merely half-finished prototypes).
The other thing is that the people that use an app store are the customers that have their hair set on fire, i.e. they come there with a specific need. Also, what's so great about (Google Play) app store is that it gives much better visibility for newcomers because popularity of the app is primarily based on the number of new installs versus uninstalls instead of simply a total number of downloads. So, even a tiny upstart app can make it to the top of the charts fairly quickly against apps that have an installed user base of thousands or even millions if the new app is useful enough for them to keep it (the install/uninstall churn is typically pretty high for any utility app or game). This mechanic is completely different from the open web where, without a serious marketing push, it's next to impossible to compete against sites that have spent years creating backlinks and reviews to their product. To put it simple, search engines lack effective ways to measure "uninstalls" and instead favor maturity (how long a link has existed) and "time on site", which leads to over-emphasis on long form and historic content.
Clearly, app stores work for distributing PWAs. The problem though is that that you still need an app wrapper for the two most popular stores (Apple's and Google's) and every store is a little different. There are also other issues with Apple's ecosystem and their posture towards PWAs. Apple just doesn't treat PWAs as first-class citizen, so people have resorted to absurd tricks to fix some basic usability issues with them (e.g. https://stackoverflow.com/questions/24889100/ios-8-removed-minimal-ui-viewport-property-are-there-other-soft-fullscreen). In my case, I just haven't bothered, at least so far. Amazon is currently the only one that doesn't require a wrapper (instead, you can just point to an URL) but it's also the smallest of the big three. Microsoft's store experience is excruciatingly cumbersome, and I'm not sure how popular it currently is, but wouldn't be surprised if in classic Microsoft style, they eventually get it right. There are also other ones, such https://appsco.pe but their volume is so small they don't attribute to much else than a place to add a backlink to your site. Now, if you are serious about making it through the app store, they each have their own community which you need to take care of, provide screenshots and regular updates, encourage positive reviews etc. Still, it's a viable way to gain some visibility for any scrappy little upstart with no marketing budget :)