Low-pass filter, is this the truth?

I've heard that the large woofers from 10 inches or larger will produce a rich/full, or, in the worst case, dull voice if their crossovers are set at above 300 Hz. Is this true?

I see many commercial speakers, such as the JBL L100, JBL L96, etc., have a high low-pass frequency. However, these JBLs, if I'm correct, use woofers as a full-range. So, this may not be relevant.
 
Usually, increasing cone area (piston diameter) increases the Mms and lowers the highest frequencies that may be correctly reproduced by a driver. Further, there are issues regarding cone breakup and beaming that limit the use of woofers as voice reproducers.

However, there are many factors such as cone material / rigidity, cone geometry etc. that can improve the voice / midrange coming out of a woofer. The following (towards the end) has a brief explanation of the various cone properties of LF drivers, that might help.

https://www.cieri.net/Documenti/JBL/Technical Notes/JBL Technical Note - Vol.1, No.3A.pdf