Yes, those companies all have strong names. For instance, a dozer is almost always called a "Cat". The John Deere name is a very recogizable brand to your average suburban or even urban citizen. But manufacturers look at things differently than most of us...
Market share and the "Bobcat" brand name are the valuable assets. Why? Let's talk about market share, first. Since such a high percentage of a skid steer loader is purchased (I think around 80%), the true benefits come when unit volume increases. Greater unit volume = lower component prices = greater profitability. The prices of engines, pumps, tires, lights, seats, switches, and hydraulic hoses will go down as unit volume increases.
In addition, all of the companies currently are building skid steer loaders themselves and have incurred and will continue to incur the design cost in order to stay in the skid steer market. Those companies would prefer to spread that fixed design cost over 50% market share instead of 25% or only 10% market share. Deere started into the market by purchasing somebody else's machine (Mustang, later New Holland) and then built their own. Volvo purchased Scat Trak. Neither company has realized their market share expectations, however.
If any of those companies were to buy Bobcat, you would continue to see "Bobcat"-brand skid steer loaders with white and black paint with red wheels. That brand-name and image means a lot to the buyer. When Ingersoll-Rand bought Bobcat a few years ago, there were quite a few people who felt that the I-R logo and name was too prominent. The decals did indeed shrink a bit over time.
Also, buying the market share leader will increase total sales of the company and provide instant bragging rights. Wall Street loves both of these.