Not sure what OS you’re on, but do you mean that you always have to send a text? My phone shows a list of options with most popular users at the top, o, like this:
So while I do have to use the link, and other person will have to click the link on mobile, then be redirected to monzo app… it doesn’t sound as laborious as what you explained! My weapon 
of choice is whatsapp, that’s why those 4 contacts (and not sure what the 5th is…) are appearing by default. I don’t even have to select whatsapp. It might work differently with SMS though.
Please note that there could be some differences in how this panel works between Android and iOS devices.
There was a bit more discussion in this topic:
https://community.monzo.com/t/monzo-me-request-pay-with-monzo-app/7710?u=avishai