This looks a lot to me like "tagging for the router".

The reason why some gates have ways behind them and others don't in this neighbourhood, is because some paths can be seen from aerial and/or street-level imagery.
I've added only the paths that can be seen from the imagery. I haven't added paths that I haven't been able to see from imagery (even if, in almost all the cases, these paths are simple B-lines from the street gate to the building).
Should I (or someone else) in the future have more imagery, then I'll complete these paths (in fact, now that I think about it, a fixme=continue tag might be a good idea to add to these gates, will do that when I can).

There are many other houses nearby with partially or completely missing entry ways that you haven't yet tagged with noexit=yes, like for example house numbers 147, 149, 157, 159, 163, 173, 179, 183, 185, 191, 193, 195, 197, 199, 209, 211, 213, 215 or 217, among others.

Adding noexit=yes tags to barrier=gate nodes doesn't make sense because:
A) A gate is not the end of a way, is an entrance to an area or property or a split between areas/properties (in this case, is the entrance to a private home). If this node would impede the way from continue onward, then it will be a fence or a wall with no gate nor entrance, and it would be tagged as such.
B) The vast majority of the nearby houses (including the two where you've added the noexit tags) have two (or sometimes more) entrances: one for  vehicles and the other being the main walking entrance. So, technically speaking, there is no noexit situation because there is an exit through the other entrance (or manoeuvrer and turn around at the front garden or directly inside the house, but that's not directly applicable to OSM routing).

And if you argue that these gates are technically noexit situations because the way on the other side isn't (yet) mapped to OSM, then I assure you that I would  have mapped the gates differently if the way didn't continue on the other side (because otherwise it would be a disused: or an abandoned: gate).