The bigger problem for Xerox was that in 1975, about five years after establishing PARC, the DOJ forced them to license their entire patent portfolio to Japanese competitors. That dramatically changed the dynamic at Xerox, which had been able to think big ideas while riding its copier monopoly.
Xerox, AT&T, and to a lesser extent Google are strong examples of competitive markets being bad for innovation. Bell Labs didn't survive the AT&T breakup in the same form, and I doubt Google would be able to screw around with self-driving cars and wearable computing if they didn't have network effects protecting them from competition.
Peter Thiel likes to make this contrarian point: competition forces you into a deflationary downward spiral where you must spend all your energy fighting with and therefore duplicating your competitors. An example of the latter would be Google Plus, which was an attempt to compete with Facebook by badly imitating them.
Government is the ultimate monopoly, and government research can spend time trying to send people to space, look back to the origins of the universe, and so on.
Xerox, AT&T, and to a lesser extent Google are strong examples of competitive markets being bad for innovation. Bell Labs didn't survive the AT&T breakup in the same form, and I doubt Google would be able to screw around with self-driving cars and wearable computing if they didn't have network effects protecting them from competition.