The huge majority of stratum 1 NTP nodes are getting their feed from GPS, so trust in NTP is essentially trust in the US Government.
A huge majority of internet routers use NTP. A huge majority of the long distance synchronous optical links use GPS to synchronize clocks. To use the IP protocol is essentially to trust in the US Goverment.
Any sufficiently self-deluded internet cryptoanarchist is indistinguishable from a crackpot.
The un-deluded cryptoanarchist would probably research how to transmit bitcoin over shortwave radio. Or better yet, use VHF/UHF moon bounce (EME). It is the only way to be safe.
IP has no concept of time, and routers only set their clocks so the logs are coherent when aggregated.
For what it is worth, I run NTP on everything that I possibly can, and I personally maintain two NTP nodes with GPS receivers. But I am keenly aware that for 99% of users, NTP time is GPS time (central authority), and not necessarily UTC (distributed), even though they are in total agreement right now.
I also patch my clients not to accept time corrections from the bitcoin network and think that the clock skew acceptance built in to the bitcoin network is insane. Or at least silly and out dated.
With regards to the suggestions of integrating NTP into the bitcoin client, I think it is a bad idea. The bitcoin client is simply not an appropriate place to put timekeeping software.
If I were emperor, I would make the client turn red if it thinks the local clock is off by more than 5 seconds from what the peers report, and refuse to run if off by more than 30 seconds.