If you race, it's pretty much an inevitability you will crash at some point. You're talking about hours riding wheel to wheel at high speeds with many other riders trying to beat them to the finish line. Shit happens. Now, more often than not, crashes aren't ridiculously bad things. Usually it's some painful road rash and maybe a broken collarbone. If you get really unlucky it can be something worse, but is almost never fatal or "career ending".
Just riding on the roads without racing, it comes down to traffic issues mostly. When you spend that much time on the roads it's likely you'll end up being involved in some sort of incident with a vehicle at some point. You can minimize this by riding very defensively and staying alert at all times and by riding on low traffic roads, but the risk is there.
Steady effort? Yes, it's quite easy, especially if you have a power meter. Just get into the flow at X wattage, and keep it in that range. Just like you get locked into 6:30 pace running you can get locked into the feel of 280W riding.
Rhythm...depends on the terrain. Obviously on flats and steady climbs it's very possible to get into a nice rhythm. If you keep power constant though, that's what I'd call the equivalent of rhythm. If you're efficient with gears you'll only minimally vary cadence by the usually 4-8rpm between gears.
I can definitely zone out when I ride uneven terrain, but I think it's a different kind of zone out than while running.
Maybe if the race is an hour long 10% climb.
The difference between a top of the line $9000+ road bike and an entry level road bike is roughly 4%. So in other words, if you are riding on an entry level piece of garbage against someone on a top of the line bike, it's like racing against someone with magic shoes that turn them from a 16:00 guy in a 15:20 guy. That's certainly not trivial, but at the same time cycling races are generally not climbs in isolation, which totally changes the game. None of that matters if you're a better sprinter and just sit on the guys wheel doing 20:00 effort while he is working at 15:20 effort.
By the time you get to a decent low end bike you would show up to a race with (1.3k-2.5k) the difference is much closer to 1-2%. Which means that now magic shoes guy is more like a 15:45 guy.
So yes, a more expensive bike wins, but it doesn't take $5k+ to get within 1-2% of what the absolute top bikes will have (and not that many guys have absolute top bikes either) so in reality the situation is rarely ever as ridiculous as 15:20 vs 16:00.
And of course if the guys on nice bikes are 22:00 guys (which, outside of races they usually are) it doesn't really matter at all what you're riding. If you're a strongish 4.5+ w/kg FTP guy you're going to be able to drop 90-95% of roadies out there on climbs even if you're riding a $300 30lb MTB.
If we are talking track middle distance, I agree, although I think there are even more complex dynamics at play in serious road races. But you're absolutely right that track races at those distance are often tactical and not a TT from start to finish.
From the title of the thread though I was thinking more guys that had running careers and now for injury or whatever can't run. Usually those guys would be doing local road races, which are almost never less than 5k and for anyone but a complete local stud are just straight gun to tape TTs.
Being in Colorado it's more the other way around, I've never not run on a hilly trail or road. It has diversity, but unless you go to trails it's more or less putting one foot in front of the other by various margins. Cycling has totally different riding styles, standing vs sitting, on the flats riding low into the wind, running (unless trails, which very few serious runners routinely bomb down) has no equivalent to cornering or descending either.
Good point about getting into the rhythm of a climb, I probably do enjoy climbing in part because it reminds me of the feeling of getting into a good strong rhythm as with running.