Maybe not "better", but useful and with a Apache 2.0 license :)
AWS should build a real serverless alternative to it or buy Algolia or something...
I would do the same if I were AWS.
The Elasticsearch Service has problems: you can't join the cluster like you can with the normal version, permissions are janky at best, it's slow, and it's expensive. For those reasons the projects my team used it on opted to roll our own elasticsearch cluster which proved a better solution long term beyond the initial annoyances. I say that to say it's not a one to one product, which will probably be their defense.
But they usually tend to build their own alternative that integrates better into their eco-system.
If you create an index, you have to pay at least 2,50€ per hour it runs.
All pricing examples were multiple thousands of Euros per month.