> Have you noticed how when you buy the ticket there's no mention of the plane
I haven't noticed that.
I can't recall ever booking a ticket on a carrier where the [scheduled] plane type wasn't readily available to me before purchasing. Typically looking at the seat map or details of the flight will show you the type (and sub-type). I wouldn't buy a ticket on a site that didn't preview that information.
I just checked the major legacy US carriers and Delta and United show it in either the Details or Seats fold-outs. American shows it directly on the schedule. For non-legacy carriers, Southwest only flies 737s [and doesn't assign seats], but shows the specific revision in a fold-out when you click the flight number. JetBlue shows it without the need for a click (as American above). If you care about the in-flight experience at all, you surely shouldn't fly Spirit, but they show it as well in the seat map.
For aggregators/OTAs, Expedia shows it in the details fold-out, Kayak in the flight fold-out, Google Flights in the results fold-out, ITA Matrix same.
I tried and couldn't find a way to book a flight where I couldn't readily see the scheduled aircraft. There's no guarantee that your aircraft won't be switched out for operational necessity, but in that event I'm sure you could decline the switch and book on another flight if you had an operational, safety, convenience, or other concern with the switch.
How do you book tickets where you don't and can't see the aircraft model before booking?