Many of us on here have computers which tell us what speed we are doing. And while I wouldn't be looking at mine while doing those sorts of speeds, it will be in the field of view if I have my
GoPro on, and if not, then Strava will list the maximum speed when the ride is uploaded to there.
It isn't hard to know what speeds you have reached on a ride, or on a particular segment.
And 60 may be irresponsible on some roads, but on others it is absolutely fine.
"High speeds" (assuming you are talking anything over about 40mph) is certainly not generically irresponsible. It is all about context. There are roads near me where 60 would be perfectly safe if I could go that fast on them. There are others where I probably could reach that speed, but anything over about 25 would be stupidly dangerous.