It wouldn’t be terrible, as long as it’s based on an open source foundation. Although that depends on the specific open source license. As long as the engine can be forked, the worst of IE6 should be avoidable.
But yes, with Opera moving to Blink, you’ve got really only two-ish browser engines. KHTML/WebKit/Blink and Gecko. WebKit/Blink are Open Source, but I think mostly BSD, so Apple/Google could migrate to a proprietary license easily.
Gecko is MPL, which IIRC is somewhat Copyleft like the GPL, just a bit less stringent.
With the Apple/Google impasse with WebKit/Blink, I think we should be able to avoid an IE6 situation, but I would feel better with a stronger Copyleft license.
As much as I love Firefox, I think Firefox has less browser share than it did back in the IE6 days.