In the South West there are lots of amazing places to stay over in National Parks such as Mesa Verde and cool towns such as Telluride in Colorado. Whether you are travelling by RV or bicycle you want to be able to join the dots between these places and not miss any of them out.
To achieve this by RV you only need 2-4 hours of driving time, whereas by bicycle you want to be putting in 6-10 hours of cycling time. Whether you are driving or cycling you want to be eating three times a day, maybe with extra snacks in between. By bicycle that means lots of carbohydrate, simply prepared with any cooking done quickly on a single heat source camping stove with nothing refrigerated. By RV that means what you would normally eat, leisurely cooked on a decent sized cooker with ingredients kept in a normal fridge. The cost of food is therefore a lot lower when cycling even if the calorie intake is a lot higher. Hence the 'fuel' comes for 'free' when cycling as you are spending less on food than you would do if travelling by RV.
Really it is an exercise in time management. Everyone does their own thing, however, I personally would not be happy putting in 20-35 miles a day. You can cover that distance before your first stop for refreshments if you put your mind to it, even if crossing the continental divide. For me a more realistic pace is to put in fifty miles before lunch, another fifty before 6 p.m. and then up to another fifty thereafter to get you to where you need to be camping out. Clearly if there is a lot to see and do that day the mileage required can come down, to half of that, e.g. to put in seventy to a hundred miles. Also, putting in the 'maximum range' of 150 or so is not realistically achievable day in, day out, but may be necessary, e.g. if heading out from Grand Canyon up to Four Corners and on to Mesa Verde where you don't want to be camping rough in very hot desert. Same in Colorado, there are parts where there are not that many National Park camp-grounds or other 'sensible' places to stay over. (When cycling it is best to have an aversion to motel stayovers as you cannot cook the same, television leads to staying up late, you are isolated from meeting nice people such as yourself and they cost money.) Really you want your rest days to be in places that are really worth the extra day, e.g. Mesa Verde where you can leave the tent set up and go on a guided tour and take in a ranger's talk in the evening. Those rest days need to be coincided with the days when you having nothing in the tank and can barely physically move.
Meanwhile, in the RV, you have pre-booked camp destinations to get to (on the bike there is rarely this requirement to book in advance). Therefore time management is not a question of 'going as far as you can'. The cyclist will be able to de-camp in less than an hour, hitting the road shortly after the morning midges have died down. Meanwhile, the RV traveller will be putting a full breakfast on, to then wash up, get the garden furniture in, faff-tidy up and make the road a lot later in the morning. They will then get to the next 'dot' on the tourist trail some time shortly after lunch, to get the best spot available in the campground. Then the garden chairs and everything else needed for camp will be set out, a proper dinner put on and so forth. This will be quite leisurely. When they are ready to settle in for a bit of light television watching for the evening the cyclist might still be some miles away from the campground with not that much daylight left. However, the cyclist will be able to pitch a tent, put some food on, eat it and get washed in less than an hour. (No garden chairs to put out.)
It really is tortoise and hare, with the 'cycling tortoise' actually seeing more of the sights along the way - the splendour of the South West is best observed at cycling speeds, with no car parks required.
If the RV driver were to push on and do the most miles possible (cyclist style) then they would be able to do LA to Denver in a matter of a few days rather than the weeks needed to do it by bike. However, in reality, you go in a RV to see the sights and they are spaced a cycle-ride apart. Although the RV driver may be quicker joining the dots between these locations, they are far more likely to have 'rest days' (not pushing on every day) and putting out garden chairs instead of pushing SPD pedals. The RV traveller's food costs are likely to be significantly higher than those of the cyclist and then there is gas/petrol/diesel on top. This is for the case of putting in 50-150 miles a day by bike, I don't think the cost analysis is the same if only going for 20-35 miles per day as you are not really 'joining the dots' at that speed.