The likelihood of there being an available class 700 in the vicinity of the failed unit (especially if the failure happens in the Core and at peak times) is slim.
In fact it is very high, particularly in the peak. There will be several, on the opposite line. Pick one, cancel it, empty it, run it on to the front of the failure, and away. Happens every day on two track railways all over the country.
they have to wait for a fitter to get there from Farringdon (assuming they can get there by train on the other line)
Fortunately there is a train every 2-3 minutes on the other line. It’s called the London Underground.
Alternatively, if the failure is at Farringdon or City TL, where the failures are most likely to be (going by history) the fitter just has to walk about 50/500metres respectively. 5 minutes max.
I don't know the location of the train immediately in front of the failed unit, but I can imagine how happy passengers on it would have been if they'd been told "Please get off at the next station so we can use this unit to go back and rescue a broken down one, oh and by the way, we don't know when there'll be another train coming through to pick you up to continue your journey".
fair point about passenger reaction - but it would be the same for any train being cancelled for any reason. In these circumstances it doesn’t matter which train is cancelled to create the rescue unit.
Thameslink is no different to any two track railway anywhere else - it’s just busier. There aren’t thunderbirds on immediate standby for the GEML from Shenfield to Colchester, Birmingham - Wolves, Piccadilly to Oxford Rd, Marylebone to Aynho, etc etc, and most of these have a wider range of traction that can’t rescue each other.