There are so many variations, this one

for example only shows a two channel programmer, and the whole idea of motorised valves is a bit last century before we started using electronic TRV heads.
I have looked at instructions, and some simply don't make sense any more, but it seems theory and practice don't always match, in theory having electronic TRV heads removes the need for hard-wired motorised valves, but it seems one can get heat through one pipe, but not worked out how as yet.
Anyway, the point is, combining both valves, as long as you have electronic TRV heads, would not matter. In fact, could be an improvement. Modern boilers should modulate, (turn up/down) not switch on/off to get the best economy out of them, and a hard-wired valve turns on/off, which is not the best way, where a TRV turns up/down, and with this house even if on/off, 14 TRV heads will not all switch together, so we get a gradual increase or decrease in flow, which better allows the boiler to gain the latent heat from the flue gases.
Old boilers, like my old oil boiler, simply switched on/off, and the return water temperature did not really matter, in new boilers, the return water temperature needs to be low enough to condense water out of flue gases and gain the latent heat. So the key to this is the setting of the lock shield valve and use of TRV heads. Been like this since the 90's, however the TRV has progressed, with the electronic head allowing setting in degrees C not some silly *123456, and being able to set when each room is heated. We start with stand alone with likes of Terrier i30 and eQ-3, then we see bluetooth added, some eQ-3 heads have bluetooth, then they connected to internet so you can use geo-fencing and the like, and then we have connection to a hub, so it will actually fire the boiler, and even smart versions which work out how long it takes to heat a room, so you set time you want room hot rather than time to start heating.
This has also changed the ideas of where to put radiators, traditionally they were under windows, but this puts the TRV also under the window, so cooled by outside, so better on an internal wall, but some systems get around this problem, by if a wall thermostat and TRV are in same room, auto linking them so the wall thermostat controls the TRV.
This has resulted in many of the old ideas today no longer being true, like not fitting a TRV in a room with a wall thermostat, again last century, today where radiators are under windows, we do fit both in the same room, and we can also connect to boilers using the ebus with the likes of OpenTherm where the thermostat tells the boiler to turn up or down not on and off, which clearly can't be relayed through a hard-wired motorised valve.
However, we have to consider cost, my home 14 TRV's so to convert all to linked electronic TRV heads looking at around £600, so I have some linked, but not all, also multi-wall thermostats, not that my system will really help as still using an oil on/off boiler, but one needs to sit back and decide what compromise will work for you at a reasonable cost.
This is the whole point of the essay, it may be easier to fit electronic TRV heads than find the fault. If you know there are other methods of control, you can see alternative ways around your problem. Out of interest, I have 5 stand-alone bluetooth, 4 internet linked, and 1 linked to boiler. I have made mistakes, if starting again it would be all Drayton Wiser, but started with silly Nest, so a bit of a hoch potch.