Please describe what the rule should do:
Disallow useless template strings, such as ${x}. The thing is this can be used as a way to cast a variable to string, which means the rule could instead be "prefer String()" or "prefer .toString()".

What category of rule is this? (place an "X" next to just one item)

[ ] Warns about a potential error (problem)
[X] Suggests an alternate way of doing something (suggestion)
[ ] Enforces code style (layout)
[ ] Other (please specify:)

Provide 2-3 code examples that this rule will warn about:

const x = "soomething";
callAFunction(123, "mamamia", `${x}`);

const x = 19
callAFunction(123, "mamamia", `${x}`);

Why should this rule be included in ESLint (instead of a plugin)?

Because eslint already had tons of no-useless-something rules, so this one would fit very well with the rest.

Are you willing to submit a pull request to implement this rule?
No unless you point me to the right resources and ask nicely and I have enough free time this week