You're a non-visa national (US citizen). You want to "channel hop" a few times and to carry a flight ticket to the USA as evidence of your intent to abide by the rules.
If I follow through with this, and cancel my ticket later, will there
be any consequences or flags with the Home Office for doing so?
There are two things to be aware of when reentering the UK from the continent...
If the Immigration Officer picks up on 'negative waves', he can give you a coded landing. It's a short-hand notation that's hand written on the face of your entry stamp. Coded landings come in all shapes and forms and I always tell people to ignore them. To you it would appear as a number, or just an illegible scribble. There's one type of coded landing that says the IO picked up some 'negative waves' and suspected that you might be trying to abuse the rules, but he didn't have anything concrete to support it. When the next IO sees that type of coded landing and you are still in a channel hopping scenario, you may get selected for secondary screening (that's a bad thing, especially at an arrival from the continent).
The other thing that can happen if an Immigration Officer picks up 'negative waves' and can't find anything immediately amiss. He can look at your ticket and curtail your leave to its departure date. If you protest by explaining that your ticket is merely a contrivance, he will get upset (that's a very bad thing). It means the curtailment scenario is basically a no-win situation for you.
The other things that can happen are (a) temporary admission, (b) full leave-to-enter, or (c) port side removal. The upside is when (b) happens because you get a brand-new leave-to-enter which expires in 6 months, regardless of how long you have been in the UK previously. There's lots of discussion about these alternatives in the archives here you you can study up on. Search on the 'removals' tag.
The 'implicit' question here is about cancelling your ticket once you are land side. There are no 'flags' or 'consequences' for doing this. People do it all the time. The exception is if you get trapped in a totally unrelated situation where somebody like the police or whoever notices that you have no provisions for onward travel, or worse that you used a contrivance to enter the country (i.e., that you are an illegal entrant). So always watch closely during your landing interview to see if the IO writes anything on the back of your landing card. Also remember that your passport is linked to the credit cards you used to purchase tickets (See Statutory Instrument 2008/5).
And finally, this detail...
My intention is to remain in the UK no more than 180 days out of 365
There are no rules that refer to a day-count or that specify a given "X" days out of "Y" days formula. The only legal point of reference is Appendix V 4.2 (b)...
(b) will not live in the UK for extended periods through frequent or
successive visits, or make the UK their main home; and