Rome in a day

Why would I want to buy so far in advance when I have no idea how long
it will take to view each area?

Because the ticket lines for the Colosseum are very, VERY long. With as little time as you're going to have, you can't afford to waste ANY of it standing in a ticket queue and then in a security-check queue. While you can't skip the security line, at least you can skip the ticket queue if you buy in advance.

One ticket covers the Colosseum, Forum and Palatine. There's no time limit on how long you spend in any of them. Understand that the Palatine and Forum MUST be visited together so you can't do one, leave and come back to do the other. On your timeline, I would buy the "open" ticket.

https://www.coopculture.it/en/colosseo-e-shop.cfm

Visit the Forum/Palatine FIRST and then the Colosseum because as of today, people buying "open" tickets will not be able to enter the Colosseum until 2:00 PM or after. You can purchase timed-entry tickets for the Colosseum but I'm not sure I'd do that in case you, say, miss your train.

The Colosseum closes at 7:15 PM in August. IMHO, this would be a long and expensive trip just for these three attractions: not something I'd personally do. It might be best to save it for another trip when you can give Rome some more time?

You only need a timed entrance for the Colloseum if you choose that option. But if you can get a timed entry in the early afternoon, I'd go with that option. You can enter the forum or Palatine at any time (but only once) within the validity period (2 days after first use, I think). The lines to buy tickets are huge. If you don't want to waste hours of your very limited time, then buy the advance tickets.

Personally, I don't consider a 5 1/2 hr train to get there and an overnight to get back a day trip, but whatever.

Not expensive. My swiss rail pass gets me to Chiasso so I only need to get a ticket from there. Personally I think spending money on dank hotel rooms is an expensive waste and wouldn’t do it, so to each his own. I don't think a 5.5 hour commute to Rome long at all. Must be a city person's perspective, it's an hour drive just to get to a decent grocery store where I live. Traveling alone, I don't want to spend any more time in Rome as the only thing I would want to visit is these sites, and seeing as they're only a few subway stops from the train station this should be plenty of time. Trenitalia has the fare at less than 50 euros one way; I've been wanting to have the sleeper car experience so this is my chance to do it on the way back.

You’ll have plenty of time to do what you want. Have fun

Why hasn’t anyone outside of the US heard of Rick Steves?

Um, we have participants from Canada, the U.K., Italy, France, Austria, Germany, Australia, to name a few. And many questions come from India.

The responses to your question were given with an eye to assisting you to have a better experience in Rome, not to dictate the terms of your trip. Most of us prefer to spend most of our vacation time seeing the sights and sampling cuisine instead of traveling on trains for extended periods of time. With that said, I think your travel time will be close to 6 or 7 hours each way.

As you say, some things are worth it to different people where those same things might not be important to other travelers. To each his own. Be aware, however, that lines are brutal at most tourist attractions in Rome, so pay attention to some of the threads on this Forum and to the websites for each attraction to get a realistic idea of wait times. The heat in August will be oppressive, just saying.

Go for it. This is an older crowd less mobile kind of travel forum
( tryin to tell you how to spend your time and money, bah! It ain't that serious).
https://community.ricksteves.com/travel-forum/general-europe/holier-than-though

No way to say how long each site but one less thing to do if you have a ticket in advance. I have gone places where I did not get a chance to see everything I had planned and ended with up with unused ticket, but so what.

I see Kathy didn’t read the insulting “visit Rome right or don’t go” post. Lol I think it’s amusing myself that in Switzerland people board the panoramic trains and pay extra for a reservation to have a big window and ride for upwards of 8 hours to view the mountains and a 5.5 hour ride to Rome has people wringing their hands that it’s too long. Riding a train to view nature rather than be IN nature is ridiculous, but riding a train to actually get somewhere is another matter entirely. The question I originally had was why would I have to buy an advance ticket to multiple areas when I didn’t know how long I’d spend at any one, but my question was , I think, answered in that when you buy the ticket online it is “open” and you can get in the line to enter when you’re ready and not a preselected time, unless you chose that option. That’s all. Done here, thanks for all who helped and to those cranky folks, I have nothing to say.

Since you're planning to stay in Rome late, you might consider an evening tour of the Colosseum (these are held after the Colosseum closes to those with normal entry tickets):
https://www.coopculture.it/en/events.cfm?id=177
Then you'd have plenty of time for the Forum and the Palatine Hill, and once you're in that area there are other interesting sites from Ancient Rome (Trajan's Market, for example) that you might find worthwhile. The evening tour would be an extra cost on top of your Forum/Palatine/Colosseum entry ticket, but it's not too expensive. The main benefit is that it's a way to see the Colosseum when it's relatively empty.

Other evening options near the Colosseum are "light shows" at the Forum of Augustus and the Forum of Caesar: http://www.viaggioneifori.it/en/ . They're kind of interesting, and they don't start till after dark so it's another way to take advantage of the later hours when you're still in Rome, if the Roman Empire is of particular interest to you.