Indeed, stating "callsign123 TCAS RA/Climb/Descent" is extremely important for me as an ATCO because it tells me to shut the eff up and leave you to it.
Forgive my ignorance but my training has always taught me that TCAS RAs MUST be complied with. As has been stated already there have been fatal incidents in the past where crews acquired visual with what they perceived to be the conflicting traffic only to hit someone else.
There have been crews who have refused avoiding action because the turn was towards the traffic, not realising turning one aircraft to pass behind the other is the quickest and safest resolution (unless using totally parallel tracks, but that's rarely practical ....I mean eventually you need to reach destination....).
What's the worst that happens if you follow an RA at altitude? You set off a domino RA on traffic above/below you, maybe get a reversal. From ignoring one? You kill hundreds of people you absolute w***er....the fact we are even having this debate is frightening. It's all well and good having the discretion to ignore one but for God sake unless you KNOW the system is malfunctioning (IE below 1,000 ft) then stop measuring your d*** and just play it safe.
This is by far the most frightening thread I have ever read on this site.