Regardless, they certainly can register all the names for you, if that's what you ask them to do, but at some point, there's an awful lot of names, and it feels extortiony to pay for them all. I was working for a MarkMonitor client when the 'landrush' for all these new tlds was happening, and we'd get frequent emails about which tlds were going live soon, so we could decide if we wanted foo.bike or foo.sexy or foo.personals, or whatever. And then, if we wanted to pay rediculous prices to get it early, or wait and see if we could get it at normal price (+ hefty MarkMonitor markup). We would almost certainly win a UDRP, but that's expensive too.
Then we got bought, and the new corporate overlords liked throwing money away on dumb domains, so foo.bike got registered by their team (and they had an actual domain team, so I got to shed that hat).
However, that's not really what most companies are worried about, they're worried about phishing or scams or misleading sites with their name; UDRP should allow those to be taken down fairly easily, although the question is always if it's less expensive to register the domain or to leave it unregistered and dispute it if it's misused.