> When you have an expression P which names a mutable place, and you execute P := X
This isn't the case, though, is it? A normal member access (or indexer) expression may point to a mutable location (field, property). However, with conditional access expressions you get either a member access _or nothing_. And that nothing is not a mutable place.
When you use any of the conditional operators, you split the following code into two paths, and dropping the assignment (since there's nothing to assign to) seems pretty consistent to me, since you'd also drop an invocation, or a property evaluation in similar expressions.
If you require P to point to something that actually exists because you want the assignment to succeed, then write code to ensure that P exists because the assignment has no way of knowing what the intention was on the left side.
If the language allows <whatever> := <new-value> --- if that compiles and executes --- then <whatever> is by definition a mutable place.
Once you introduce this misfeature, mutable places no longer have the property that they all record the assigned value and keep it until the next assignment.
Now, sure, you also don't have that property when you have operator overloading that allows assignment to be coded by the programmer; but that's a design decision under the programmer's control which affects only that code base, not the entire language and all its users.