If the input provides mic bias already, adding external biasing circuitry in front will only ever make things worse, given that both bias resistors are in parallel small-signal wise. Less signal, more distortion.
Mind you, the mic bias voltages generated by onboard audio in particular often leave much to be desired in terms of cleanliness, generally dominating input amplifier stages by quite a bit even though these can be rather more noisy than you'd really want as well. Occasionally you'll also find performance marred by ground noise from internal ground loops.
Since those same inputs tend to accept some rather healthy input levels at the same time (assuming a lower step of preamplification is used), using an external preamp seems like an attractive proposition. Usually about 20 dB with low output impedance (to dominate any noise coming in via bias resistors) will do the trick.
While microphones based on small electret capsules are never going to be the last word in noise level (it doesn't get an awful lot better than about 30 dB SPL, A-wtd), the poor linearity at high levels can in fact be addressed:
Siegfried Linkwitz proposed hacking the capsule itself to rearrange the FET amplifier circuit from common source to source follower - which basically works but is fiddly and may take a number of attempts before producing a capsule that is actually working and not just ruined.
Johne Conover suggested making use of a second external cascode JFET and letting semiconductor physics sort things out
(see around Fig. VIII and onwards). For good results, said second JFET should have a somewhat larger Idss and a substantially higher Vp than the one inside the capsule. I imagine that going with a higher supply voltage would enable using even higher Vp parts than the 2N5484 he had; also some gain trimming is likely to be required for good stereo channel matching since output level would depend directly on transistor parameters known to be potentially quite variable.
Arguably it's all a bit of a moot exercise these days, as you can get a decent enough pair of phantom-powered pencil condenser mics around the 100€ mark on this side of the globe, with capsules that are like 3 time the size in spite of being called "small diaphragm", giving more attractive self noise and level handling right out of the box.