Rabbits don't have to eat their cecals. Also a rabbit should not eat cecals that have fallen onto the floor. If the rabbit eats cecals that have fallen onto the floor that is a good way for the rabbit to get coccidiosis. Cocciciodis is often gotten by the rabbit ingesting fecal matter either from the floor of the cage or from eating food that has been contaminated by the fecal matter or by drinking water that has been contaminated by it.
When rabbits eat cecals they eat them as they come directly out of their bum. When they are eaten in this manner they cannot contract coccidiosis. Research studies have been done on this.
Eating cecals is a way of gaining more protein and energy out of their food. If the rabbit is getting enough protein they may not need to eat the cecals. It can also be a way of conserving water.
What you may be describing may be soft stool and not necessarily cecotropes. Cecotropes look like a small grape cluster. Where as soft stool will tend to be just one big glob.
Also be careful of feeding too many grains such as oats. These are made of starches which are alsoa form of sugar. Sugars tend to promote bacterial growth in the digestive system. Too much bacterial growth in the digestive system can cause diarrhea. Grains are also low in fiber. So its not just veggies and fruits you have to watch out for.
Another cause of soft stool can be stress. If it is hot that can cause stress. Changing the diet or moving your rabbit can cause stress.
Another cause of soft stool can be mold. Two places to check are any hay or bedding you may be using or the pellets you may be using. It only takes a small amount of mold to cause diarrhea. So hay that you feed your rabbits should not smell moldy or have a white powder look anywhere on it. If you use straw or hay as bedding it should not smell moldy either because the rabbit may eat the bedding. Also smell the feed to see if it smells moldy. Always keep the feed in a cool dry area to prevent it from molding. If it has sat for over a month it may tend to get moldy. Just because you can't see the mold doesn't mean it isn't moldy and won't cause problems. The nose is a much better indicator. If you had a batch of pellets that didn't look moldy, but smelled moldy and you stuck them under a microscope you would probably see little pieces of mold on the pellet that were undetectable to the naked eye. Those small pieces are enough to potentially give your rabbit diarrhea.
Don't cut back on the amount of feed you give. Give a little hay such as alfalfa hay, red clover hay, or timothy hay in addition. The roughage and extra fiber should help stop the diarrhea.
If you're worried about your rabbit stepping in the poop, then get a cage like the ones displayed at:
http://www.bassequipment.com
Wire floored cages won't hurt your rabbit's feed unless you havea very large breed that gets over about 11 pounds when it is an adult. The wire floors help keep the rabbit cleaner, which is more healthy for your rabbit. And it makes them easier to clean out. Prevention is the best way to keep your rabbit healthy. And a clean cage and clean waterer are two of the best ways.