how big of a probe feed to use with microstrip antenna?

can I use a coax with inner conductor (probe) radius of 4mm to feed microstrip antenna? Is there a limit to how big of a coax you can use with a microstrip?

The bigger the probe radius, the better the bandwidth.

A related question, for probe inner radius 4mm and outer radius 9.16mm for air substrate, the cutoff frequency is 7.25 GHz. My microstrip is getting bandwidth between 4 and 10.5 GHz. So, shall I ignore all frequencies over 7.25 GHz since coax won't support them? So, my actual bandwidth become 4 to 7.25, instead?

Thanks.