What I have heard about many commercial PCB routers - especially LPKF! - is that they require a competent fulltime hire just to keep the machine operational. So while in theory, it sounds like a "press a button" thing, it doens't seem to work out that way. Actually, I have never seen an operational PCB router! They always seem to be in the "just now it has this and this little problem" state, because of the lack of maintenance resources.
It's possible that easy-to-maintain "it just works" PCB routers do exist - no law of physics say it's impossible - but you have to really do your homework before committing to expensive crap like LPKF.
The very reason, after all, people buy them is to make small scale quick-turn PCBs easily and cost-effectively, and having to put $50k-100k/year to maintenance is a big surprise for small players.
So, IME, etching, even though messy, is more reliable. You still need a CNC drill however which is another can of worms. Ours is a partially home-made modification. In any case, a CNC drill is orders of magnitude easier to get right than a precision router.
Even local, expensive quick turn around PCB services tend to be cheaper at the company level where every worker's time has a price. OTOH, in some cases, quick adapter/test boards are required in just hours, in which case your own minifab is a requirement, as a two or three day (incl. shipping) PCB service would cause unproductive time slots.