Oh how I agree with that. Apart from the feedback issue the other guys in the band prefer their monitors bass-free. My backline is plenty for me. And them.
This has not been my experience playing in, or running sound for big bands. Unfortunately most big bands want lots of bass in the monitors; often enough to significantly degrade the sound.
Mic'ing an upright is problematic when the sound is sent through any speaker that are near the bass; it does not matter if it is a bass amp or monitors. The upright bass is not a very loud sound source and the microphone responds to which ever sound is loudest. If the sound coming from surrounding instruments is louder at the mic than the bass, then the bleed from those instruments will be louder than the signal from the bass. If the sound coming back to the mic from the amp or monitors approaches the acoustic volume of the bass at the capsule, then the signal will be significantly degraded and gain before feedback will be very low. Distance and/or isolation are very important tools to draw on, and both are typically in short supply in a big band environment.
I will suggest again: If the channels are available, send a mic and pickup signal to FOH; with the preference to use the mic for FOH if possible. Typically sound check does not allow a lot of time to fuss with the bass to get it perfect. Either the mic will work with minimal effort or the bass will sound bad for the duration of the concert. Sending the pickup provides options that an experienced audio tech can work with.
If bass is desired in the monitors, the signal from the pickup has the best chance of working without causing problems, but again the audio tech should have options instead of being potentially forced to provide bad audio because the bass player wants to call the shots.
If your amp is pushing the band without PA support, do whatever you want because all of the blame or praise will fall on you. If you are running through the PA, it's a team effort and I would argue that the audio tech deserves a chance to do a good job.
Usually if the sound is too loud or the mix is not perfect, the audio tech gets the blame. But in many situations the problems are caused by musicians making decisions that deprive the audio tech of the power to do the job well. For example, if one or more of the musicians on stage plays louder than the mix should be, the audio tech cannot fix it. If someone selects equipment or processes their signal in a way that significantly degrades their sound, there is nothing the audio tech can do to fix it. If you only send the audio tech a mic'ed signal you may be sending a signal that is virtually unusable in some settings.
Many of us know how wonderful an upright bass can sound through a mic when we play solo. And of course that is the sound we want and crave. Unfortunately the results you can get with a mic and recording equipment do not translate to noisy environments where the mic is used in conjunction with amplification and sound reinforcement. The noisier the environment in the immediate vicinity of the mic, the less useful it will be.