For what it’s worth, I have an acquaintance who was in London earlier this year, dropped 40k pound at New Bond, got a Kelly (don’t know specific specs), in the span of two weeks.
Personally I think it can be done either way, and everyone should do whatever makes the most sense to them!
What is always true imo is 1) you are the one shopping and parting with your money, so what makes you happy should always be the most important, 2) there’s always some luck and timing involved; things that are entirely out of your control. So it’s no use being too obsessed - will only cause you unhappiness. Yeah it’s easier said than done, but do try to relax and be patient! 3) purchase what you love regardless of the bag is really the only way to ensure that you can enjoy those purchases 100%, and at the H price point that’s pretty important (of course if you have infinite pocket depth feel free to ignore me

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ETA: also imo, for a city with multiple boutiques, even if there is one store that is supposedly “easier”, if that were truly the case and word gets around, then over time it will all even out because there’s no difficult barrier stopping others going to the “easy” store and making the supply and demand reach a new equilibrium. If you can hop over to another store easily, so can everyone else.