As of 2022, within the vicinity of almost any mechanical watch, there are likely to be tens or perhaps hundreds of inexpensive satellite-based location-estimation devices (GNSS) - inside smartphones, vehicles, internet-of-things devices, etc. There are also purely radio-based clock signals.
Those receivers, which are usually entirely passive (receive-only) measure accurate time signals as a component of their functionality.
It's important (and useful!) to track time accurately, and there's certainly nostalgia/envy aplenty to be had in the notion that our ancestors (who may have grown up in an era prior to GNSS) express their devotion through the symbolic hand-me-down of mechanical watches, but... perhaps it's sensible not to be pressured by the hype and -- nowadays -- irrational financial cost (of which, despite the ostensibly factual nature, I think this article is part).
I guess a less trite and more actionable way to state this would be: consider saving yourself the economic cost of a mechanical watch (first-hand or second-hand), and instead spend literal time with the person you love and intended to provide it to - potentially using the amount saved to help fund and remember the moment.
Similarly: if that person would have preferred an expensive timepiece to actual time spent with you, then.. I suppose it's a good deal either way?