It's a nice dream. At Google Cloud Next last year, the vendors kinda of came in two buckets. Datadog, and everyone trying to replace Datadog's outrageous bills.
FWIW the "datadog doesn't like otel" thing is kind of old hat, and the story was a little more complicated at the time too.
Nowadays they're contributing more to the project directly and have built some support to embed the collector into their DD agent. Other vendors (splunk, dynatrace, new relic, grafana, honeycomb, sumo logic, etc.) contribute to the project a bunch and typically recommend using OTel to start instead of some custom stuff from before.
They support ingesting via otel (ie competing with other vendors for their customers) but won't support ingesting via their SDKs (they still try very hard to lock you in to their tooling).
Yeah their agent will accept traces from the standard Otel SDK but there is no way to change their SDK to send the traces to anyone other than Datadog when I last checked a couple(?) of years ago.
I mean I understand why they did that but it really removes one of the most compelling parts about Otel. We ended doing the hard work of using the standard Otel libraries. I had to contribute a PR or two to get it all to work with our services but am glad that's the route we went because now we can switch vendors if needed (which is likely in the not too distant future in our case.
OTel is a bear though. I think the biggest advantage it gives you is the ability to move across tracing providers