Is it too risky to book Colosseum ticket/tour on Day 1?

I would definitely put any big visits a day or two after arrival. You will probably be jet-lagged and that will give you time to recover. Also, if the flight is delayed a day, then you wouldn't make your reserved tour. Generally, I don't have any big plans the day of arrival, just walk around and get to know the area I'm staying in.

2 couples we know, one on a trip to Italy and one on a trip to London, had their flights cancelled on the same day. That's 100% of the people we knew traveling home from Europe that day. You should always assume that the same thing can happen on your trip to get to Europe. Wait until you get there to make reservations for your arrival day-I think some sites, like San Clemente Church, would have same day reservations available.

I will fly from Greece to Rome on Day 0.

Consider how much money you’re willing to risk if you don’t arrive in time or don’t travel as planned for the visit then decide which activities to book. There was no doubt that I would be traveling in Israel right now until the unexpected happened. Some costs associated with that trip were uninsured.

I did, however, land in Italy today. Having the need to travel from Milan’s airport to Lecco I considered the options and decided on trains - specifically booking one for 1 & 1/2 hours after my arrival. We departed the plane at 6:02 (18 mins early) and I was at the train tracks by 6:30 (1 hr and 13 mins early). Passport control took less than two minutes which also includes processing through the electronic gates - scan passport, move forward for photo, then wait for next available agent. Yes, I said less than 2 minutes total. The passport control officer was done with my passport before I could move my hand away after giving it to him.

Thankfully my first train was the Malpensa express which had a 6 hour window for use. The agent said that I could board an earlier train. Also, I did not purchase my train ticket until my international flight was backing away from our departure gate. Not the same as scheduling a visit to the Colosseum. The point is we never know what’s possible.

If you just fly from Greece to Rome the day before, the risk of a major issue seems lower. I mean, at worst, you could visit the Colosseum with the previous day's clothing, right? As long as you're not planning the Colosseum on arrival day - and I understand you are not - I think you are good!

The thing is, tickets to the Colosseum are hard to get. If you plan that for Day 0 and miss your entry time, will you be able to get a new ticket for Day 1 or Day 2? You'd have to go to one of the new ticket booths, and the advice is to go very early, since same-day tickets are limited. I don't know whether that approach assures you'll get a morning entry time, much less an early-morning entry time.