It is possible to sandbox C++ to some extent, yes. However,
1. It was not designed for that from the beginning, so the result has some tradeoffs (not all C++ code can run in a sandbox, performance is not quite the same, etc.).
2. Practically speaking, if you have a web browser with one sandbox that you spent huge efforts on (and all do), adding another sandbox means a lot of additional effort and risk. The risk comes from the fact that each sandbox will have vulnerabilities, so having more sandboxes means more of them.