It is not necessary to have contributors assign their copyright to you, as long as the contributions are licensed under sufficiently permissive terms that permit you to use them and distribute them under (or compatibly alongside) your project's existing license.
The GNU project does this for at least two reasons:
Only the copyright holder can litigate against copyright infringement. If the GNU project didn't hold copyright on some piece of code within GNU software, they could not sue to stop a GPL violation on that piece of code.
A much more complex concern has to do with joint authorship, which occurs under special circumstances in some jurisdictions (including the United States). If certain conditions are met, then a work with multiple copyright holders can be unilaterally modified, distributed, and relicensed by any one copyright holder individually, sort of as if they were the only copyright holder. The law around this subject is complex and I'm not completely familiar with it, but this is very likely the complexity that GNU hopes to avoid by being the sole copyright holder.
The notion of having a university or employer disclaim copyright interest is in any case very important, since otherwise the contributor may not have the right to submit their contribution to you at all, because they have an employment contract that grants copyright control of works they create to a third party.