Not able to edit Test Plan after running it at least once

I assume the reasoning is that the previous test runs would become meaningless if you edited the tests after running them. You would not know which version of the test the previous runs were against. Unless you started versioning tests, and that's a whole other problem!

I see your point. Another solution could be here: to clear out particular test result once you updated test case. Whereas if you create a copy of test plan and update 1 test case there, all results are cleared.

Would you want to keep an old version of test case? I can't think of a situation where I would want to..

It does seem like it'd be useful to know that a test passed a number of times before updating it, and then it started failing.

Clearing test results doesn't seem like it should be done as a side effect of something else. It seems like you should only be able to get rid of test results by deliberately erasing them.