I don't think that there are any 'DSP applications that the fixed point can not handle.' Digital designers carefully take the accuracy and range of fixed-point numbers into consideration.
Fixed-point numbers are continuously scaled up to avoid bit loss, and down to avoid bit overflow. This happens after every single mathematic operation to maximize the number of bits in use. During this time, the designer keeps track of the scaling up and down. It is a very meticulous, thoughtful, and intentional process.
At the end of the algorithm, whatever remaining scaling hasn't been corrected, the designer can either perform one scaling operation, or put the results in block notation.
Fixed-point is very powerful. It can lead to greater resource effeciency and can even decrease total error. However, it requires much more careful planning and design than floating-point. Which can be slow and costly for a project.
This is why most companies break the job into two positions: algorithm development and digital design. Then there are people like myself who live in the middle between the two.
In conclusion, I don't think your assumption is correct. Not in my experience, at least. And I have worked on some very complex algorithms on very resource restricted platforms.
Hope this helps! Let me know if I can clarify anything.