"Go around, contact xxx approach"

So I just finished a flight with a missed approach. And I found the current phraseology kind of awkward: When I announced G/A, tower instructed me to make right traffic and handed me off to approach. But then the approach told me to turn left. So I wonder if the ATC commands can be adjusted to make the tower-radar cooperation more realistic and improve efficiency.

My idea is as follows:
(pilot announced go around)
TWR: (apart from “left traffic” and “right traffic”, there is a third instruction “contact xxx approach”, which only shows up when radar is present. ) Roger, fly runway heading, contact xxx approach on xxx.xx.
(The pilot replied and switched to approach.)
P: xxx approach, (callsign), executing missed approach. (Shows MA on progress strip)
APP: (callsign), roger, expect (type of approach).

This saves the trouble from handing off, distinguish MAs from departures and therefore increase efficiency.

(I don’t have votes left so I’m just proposing an idea)

Hey mate! I think this would be a really useful command to make controlling better.

Here’s a very similar topic. Maybe we can collect our votes there 😉