The minimum channel length is defined by the foundry for a particular technology process.
More often than not, minimum channel lengths are used for digital blocks only, since they are the high speed switching blocks and also because they occupy, as a rule of thumb, around 60-70% of a die area.
In analog design, where high performance is a criteria, minimum channel lengths are seldom used. In fact higher lengths are required to increase the output impedance of a transistor which is required to achieve good gains, isolation from supply variation, etc.
Remember that Id is a function of channel length modulation factor "lambda" which in turn is inversely proportional to channel length 'L'. So, for a current source transistor, more the "L", lesser will be the variation in Id with supply.
Hope this helps. You can always refer to books like Razavi for more insight on analog design.