They are. Those stopover accommodations are all set when you arrive. They know their clientèle...
Have you ever done this before? Icelandair flights from the East coast fo KEF are very short for transatlantic flights at five-and-a-half hours, and a 9pm EST departure time with a 6 am local time arrival means that your still not-adjusted body clock thinks it's 2 am when you arrive - just a bit past bedtime for most folks, and before the point of no return that is a sleepless night.. So the trick is to not (try to) sleep during the flight but only right after arriving at the stopover hotel. This will make most people adjust to the time difference pretty well. It does work, trust me on that.
Speaking of Icelandair: They sometimes have sales on their premium product as well, While these seats aren't contemporary business class flat beds, they allow for a great deal of recline and are pretty comfortable. With sale fares dipping below $1000 roundtrip sometimes, they offer value that's hard to beat.

Here's my time-tested order of preference for minimizing jetlag on eastbound transatlantic flights:
- lie-flat seat and selecting the departure point so there'd be at least seven hours of sleep. For example, when flying LAX-Europe on AA I take a nonstop or connect in DFW or MIA and not in the Northeast (JFK, PHL, CLT) as that will ensure longer flights of at least nine hours block time where I get enough sleep between meal service and breakfast.
- lie-flat seat and backtracking, flying one of the ME carriers or TK. Departing from the East coast, that's the only choice of ensuring enough sleep in the air.
Disadvantage here is price and total trip duration is unnecessarily long. Advantage: I get a nice lie-flat seat for all of the trip (no shorthaul flight in a 30in-pitch seat) and arrive at my destination all rested and freshened up (shower in the lounge during the layover). This is something for the mileage hounds on here, not something 'normal' people would do.
- economy seat and breaking the journey: Here, Icelandair's offer is outstanding, Defunct WOW had the same business model at an even cheaper price point.
- economy seat and daytime flight. Necessitates overnighting in London as arrival at LHR is so late it precludes most connections. Advantages see above, no sleep necessary on the plane. Disadvantages: limited flight selection, impractical schedules depending on point of origin in the US (you certainly do not want overnight layovers at both ends of that transatlantic flight!), LHR layover can get pricey depending on dates (the Sofitel is now at least EUR 150 on its cheapest days), having to deal with LHR which for someone with no status is not a pleasant experience (long lines for everything).
- economy seat and connecting on or departing from the East Coast- the standard. I can't sleep well sitting up and need a day to recuperate from travel when doing this.