The main benefits page (of which this is a sub page off it) states “benefits on your card varies by card type and by card issuer. Please refer to your issuing financial institution for complete coverage terms and conditions or call the Mastercard Assistance Center at 0800-96-4767 for details on your benefits” so it may not be available on the Monzo card. Many of the benefits are only for MasterCard World and MasterCard World Elite card types.
The word from Monzo is that they don’t offer this service, but it’s something they might look into.
From my point of view, as an emergency option if I’m travelling and all of my cards/cash gets stolen, it would be great if Monzo could Western Union some money over to me (even if I pay all the costs - I’m not asking for anything for free).
I used to carry travellers cheques for this purpose (Amex guaranteed to Western Union money to you if you lose the cheques). But travellers cheques acceptance is so limited these days that they’re a bit of a liability.
You could probably do this yourself (it costs a fiver)
It appears W.U. accept bank transfer, so you could log in on a phone and transfer some funds. Then collect it using the code and some ID.