JFET saturation current
Is it possible to analytically calculate Idss for JFET

Yes but only if you knew the values of all relevant parameters accurately enough. And not their average value but the actual value of the JFET you're analyzing.

Problem is, many of those parameters vary a lot so it would take quite some effort to determine all those parameter values. It is much less effort to just measure the current of that particular JFET.

That large variation in current between similar JFETs also means that you should only use a JFET as a current source if you do not care much about the actual value of the current. For example if you just need a current of a couple of mA which needs to be fairly constant over supply voltage variations but you do not care much about the actual value of the current, then a JFET might be suitable in some situations.