This is an interesting and evolving area, but in my experience the verdict usually fall towards the freelancer having legal right to use their own sound effects library as a work-for-hire.
As a freelancer, if you purchase the royalty-free right to a sound effects library and are hired by a company that does not have their own library, you can use your own as long as they are used in synch.
Some companies do provide their own library and some companies like to purchase either the sounds or library you used on their project just to be 100% clear/for good housekeeping.
An easier way to understand all of this is to liken it to a painter (sound designer) and the patron (client). A painter may bring his own paint to paint the patron's portrait. Sometimes that is enough, sometimes the patron supplies or purchases more paint (wider variety, higher quality, etc) for the painter, in addition to commissioning the painting.
All in all, to support the sound effects industry, it is nice
This is what Sound One did - they supplied a massive library (200k+ sounds)that could only be used on Sound One projects. Unfortunately, Sound One has shut down temporarily and now there are a ton of freelancers here in NYC looking for work.These freelancers are not allowed to use Sound One's library in their own projects and projects for other clients.
I am the Library & Licensing Specialist at Pro Sound Effects, so I handle licensing issues of all sorts on behalf of our catalogs (Blastwave FX, BBC, Foundation, etc). I hope this helped and happy to try to answer any other questions related to sound effects licensing.