I'm a regular coffee drinker, so it makes no suggest I go home and make a coffee several times a day when I'm out maybe 30 miles from home. I think people who can make coffee at home aren't going to forget that just because this service is available.
The idea of ordering in advance then picking it up sounds fine to me for when I know - or suspect -there'll be a queue. Also, you'd be surprised how often I get asked my name when i'm ordering, but when the drink is ready they just shout out "grande latte" which is often what more than 1 person has ordered so it causes confusion/grabbiness. Ordering in advance would seem to make it more likely they'll put a name down, though I could be wrong.
My only problem with this service is that I already tried it (Costa do this in the UK) but they'll just chuck your coffee away (without a refund) if you don't get there within 15 minutes of ordering; it's likely I'll be using public transport to get around and you just can't rely on that so unless I order as I walk down the street - perhaps stopping, to be safe - I'm in danger of losing my money, and I'm better off just ordering when I get there.
Oh, and you need a web-page for this - I don't really install apps any more, as they're like web-pages I can't block the trackers/javascript etc of.