Does declining housekeeping deny housekeepers of their income?

It varies a bit. Some references that may be of interest:

Quora: Is the hotel housekeeper better off if I have my room serviced or if I don’t?

"Pay-per-room" cleaning can save time and labor expense while increasing service scores and room attendant satisfaction

The exact details for a US hotel are going to depend whether housekeepers are paid by the hour or per-room, whether the property is unionized and what terms the union contract requires, whether housekeepers are hotel employees or outsourced, and other particulars a guest has no real way of knowing. If enough guests decline service, the hotel, which is always looking to reduce labor costs, will surely compensate by sending staff home early (to the extent permitted by contract) and eventually employing fewer housekeepers. Whether your declining service contributes to that outcome directly on a particular day or merely indirectly is impossible to determine, but you are in some way contributing.

As a clue, some hotels will even offer you loyalty points or food and beverage credit if you decline housekeeping services. This is not something they would do if it didn't reduce their costs by more than the cost of the points or credit.

Now, I don't think there's anything wrong with refusing housekeeping service if you simply don't want the service. There's no ethical obligation to order lots of room service because it helps keep waiters and cooks employed, nor should one break air conditioners to contribute to the livelihood of hotel engineers. But there's also no need to avoid receiving housekeeping out of a desire not to be a bother.

Housekeeping is not "unnecessary work." If the hotel provides housekeeping services, it's not some kind of extra favor: it is literally the precise work that housekeepers are paid to do. If you take advantage of the service, there are things you can do to reduce the workload and make housekeepers' lives easier, such as not being a giant slob (which I presume someone as conscientious as you is already doing), declining fresh sheets if you don't want or need them, and leaving a tip for the housekeeper.

It's also worth noting that many hotels will eventually want to check on the room if you keep the Do Not Disturb sign up for several days in a row in the interest of safety and security, so you're likely to hear from them eventually.

I am a housekeeper in the UK we are all payed a 0 hr contract. If you opt out from your room being turned down or cleaned our wages are less that week..as for tips we are hardly ever tipped we almost always get overlooked we have a tip jar that we have kept from a year ago and have saved £10.12 p between 5 staff.! It's strange that when ever I go away abroad I tip room staff but never do myself in the UK .tipping restaurant's is the norm in the UK, not housekeeping. !

My Wife is in management at a hotel here in Canada after working for years in house cleaning. While I am unsure if the USA is different in the way they operate (as some states most surely are) here in Canada she is paid by the hour. Since the job can either give long, difficult days, or short easy days, you don't even really get what is considered full time hours most of the time, unless your hotel is really busy.

That being said, when she has 16 check outs and 9 stays, she likes having a few more stays decline service as it makes her job a little easier. But when the hotel is really slow, that extra time would be nice for the paycheck.

Remember to tip your housekeeper too! It's always a nice surprise for them and makes them feel appreciated, plus if you stay for a long time and have the same housekeeper he/she may even go a little extra to ensure your room is clean.