The basic problem is that identifiers can be either types or variables, and without a keyword letting you know what kind of statement you're dealing with, there's no way of knowing without a complete identifier table. For example, what does this mean:

foo * bar;

If foo is a type, that is a pointer declaration. But if it's a variable, that's a multiplication expression. Here's another simple one:

foo(bar);

Depending on how foo is defined, that could be a function call or a declaration of a variable bar of type foo, with some meaningless parentheses thrown in.

When you mix things together it gets even more crazy. Check this example from this article:

foo(*bar)();

Is bar a pointer to a function returning foo, or is foo a function that takes a bar and returns a function pointer?

let and fn keywords solve a lot of these ambiguity problems because they let the parser know what kind of statement it's looking at, so it can know whether identifiers in certain positions refer to types or variables. That makes parsing easier to write and helps give nicer error messages.

any new keyword could break backwards compatibility

Wouldn't that happen anyway with variable and function names? Any type other than primitive/built in ones are usually camel case so lower case keywords are more likely to clash with single word variable and function names, unless you restrict the cases of those too or allow keyword overriding or something.

At least in C#, you can define variables with keyword names like this:

var @struct = "abc"

I think in Kotlin you can do the same, and even include spaces with backticks like val abstract class = "abc"

I'm not sure if other languages allow that, regardless it should be rarely used.

Ah I was misunderstanding the problem. And learned something new about C#, seems in order to avoid breaking existing code they introduce "contextual keywords" var being added later, it is a contextual. You can create a class 'var' and the compiler will prefer it.