Lab to RGB conversion, and RGB colour space default

No. It is not possible. The sRGB color gamut can’t be made wider. Making it wider makes it something else, Adobe RGB for example.

The reason to use a Lab based workflow is to reduce the effects of cumulative rounding errors and facilitate tools tuned to make adjustments based on human perception.

In typical implementation, cumulative rounding error is reduced by using floating point values rather than integers. Human perception is accounted for by the LAB model itself.

The goal of the LAB model is equations that account for human perception, so it is still numerical of course.

Using the LAB model means that you only have to deal with out of gamut colors once at the end of your pixel pipeline not each time an out of gamut value occurs. Effectively, this means out of gamut can be adjusted at the output device level, such as sRGB for displays and CYMK for print.

Keep in mind that most work is not color critical and handling out of gamut color automatically is almost always good enough. It is not good enough when you can actually see the difference and the difference is wrong and all the other reasons things can go wrong with color are known not to be the problem.

This is almost never the case in photography.