It can: https://openrouter.ai/docs/guides/features/server-tools/web-...
It's apparently even the default these days (which makes sense, as it's usually better in my experience).
Another example might be all the managed agent features, where you get a VM + model, right now it's mostly Google and Anthropic that have this offering.
The service tier is another, where Google, Vertex, OAI, Anth offer it but only OAI and Google offer flex service tier and not all models from them get it.
OpenRouter for me is an abstraction over that complexity, they will have their work cut out for them.