I am a busy professional with a stressful job and long hours though not in the city, and these days I work part time (for various reasons but not least so that I can protect my mental health from burnout due to the stress of the job), which as a single parent limits my finances to the point that sun holidays every 12 weeks is sadly unaffordable. However I would jump at the chance to do exactly what you’re doing if I could so I definitely don’t think it’s madness! I find holidays abroad to be an excellent stress buster and I have never regretted money spent on travel personally, I think it’s money excellently spent if you have it. I personally don’t know anyone who takes that many trips abroad though!
I am limited to school holidays currently which doesn’t help with the expense of travel, so usually these days we go for a sun holiday once a year in summer, usually somewhere reasonably close such as to a Greek island or Italy or the Canary Islands or maybe France/Austria/Spain etc, though we had an amazing trip to Mexico once. Would love to take some more far flung breaks away but affordability plus the pandemic have limited that in recent years, I travelled a LOT as a young person though to more exotic destinations, took a gap year, went backpacking lots at uni etc, so don’t feel I am missing out, and my son simply does not have the travel bug in the way that I do and would be equally happy with a week in the Canary Islands as Thailand etc. plus he is generally quite a homebody. I try and make the annual summer holiday 10-14 days if possible but some years it is just a week. Occasionally we have managed a week away skiing in the winter, or for another sun holiday too during one of the half terms, but holidays have definitely had to be cut back here since the pandemic/Truss/cost of living crisis.
For other breaks we often travel to other parts of the U.K. to stay with my parents or siblings or friends, so at least we are getting a change of scene, or occasionally they come to stay with us. Sometimes we’ve even stayed in an hotel, although in general I don’t find a U.K. holiday to be restorative in the same way as a trip abroad somewhere sunny, partly due to the weather but also just lack of novelty/difference I think (in the past I’ve been disappointed in Barbados and Singapore as they felt too much like the U.K. had been transplanted somewhere sunny, and the Channel Islands are exactly that), and unless you stay with someone it’s just as much money if not more compared to a sunny European break abroad.
As my son nears university age I’m hoping to do a bit more travelling again, but I will have to try and up my working hours again to afford it although it will be nice not to be so tied in to school holiday times and the expense of that.