Market forces.
There are far more programs targeted specifically at Linux than at BSD. A lot of software is software-portable from Linux to BSD, but many software producers do not bother.
If a piece of software isn't open source, ABI emulation is one way to make it run, which is what the BSDs do.
The reverse case simply doesn't happen enough to make it worthwhile to add such a binary ABI compatibility layer to Linux.
Once upon a time, when x86 Unix held a market majority over Linux, Linux had the iBCS layer, which allowed it to run binaries built for SCO Unix and such. Once Linux took over the market, this feature bitrotted, and eventually got taken out; it hasn't been part of Linux since the 2.2 days. The SCO lawsuits helped usher this feature out of Linux.
So, Linux did once have a similar feature, but for a different OS. There's no technical reason it couldn't happen again, but it's not likely to unless the market positions of BSD and Linux switch for some reason.