1. Both the JVM and CLR have different focuses in terms of startup speed, which matters more on the web than anywhere else (this is one reason Java failed on the web). JavaScript and WebAssembly are designed to start up quickly.
2. If you have both the CLR and a JS engine in the same browser, you have problems with cross-VM GC cycles and the overhead that causes. That is one reason why WebKit opposed adding Dart bindings, for example. WebAssembly is designed to integrate with existing JS VMs.
3. Both Java and the CLR are open source, but both are patented. Both have licenses for those patents, but this has been the cause of much debate, as there are corner cases in those licenses (e.g. if you do not fully implement all of the VM per the license, you may not fall under its protection). This could be resolved - all existing patents could be offered up to the public domain - but I don't see Microsoft or Oracle (and there may be others with patents) doing so.
2. If you have both the CLR and a JS engine in the same browser, you have problems with cross-VM GC cycles and the overhead that causes. That is one reason why WebKit opposed adding Dart bindings, for example. WebAssembly is designed to integrate with existing JS VMs.
3. Both Java and the CLR are open source, but both are patented. Both have licenses for those patents, but this has been the cause of much debate, as there are corner cases in those licenses (e.g. if you do not fully implement all of the VM per the license, you may not fall under its protection). This could be resolved - all existing patents could be offered up to the public domain - but I don't see Microsoft or Oracle (and there may be others with patents) doing so.