I have been replacing failing 2 wire to 3 wire(aka grounded) power cords on tube equipment for decades, especially vintage guitar/bass amplifiers with no problems with the use of said electronic equipment + performing AC chassis leakage tests before releasing the repaired audio equipment to the customer..
And in one instance, by doing so probably save my customer`s life when his mid sixties Fender Deluxe Reverb guitar amp`s AC power switch developed a bazaar carbon burn through trench in the plastic housing`s back from the switched load(power transformer`s primary wire) terminal to one of two nearby rivets that held toggle switches plastic housing to the metal front of the switch and on to the chassis, which if I hadn`t power cord grounded the amp he would have had full line voltage on his body and if he touched another grounded musician, equipment, or microphone while touching his guitar strings, the resultant shock might very well have killed him !!
Instead, when he flipped the amp on, it promptly blew the 2 &1/2 amp mains fuse saving him from a nasty shock.
When I electronically restored my Mc. MC 30`s, and MC 60 yrs. ago, I replaced all three power cords with modern grounded power cords, and have no ground loop issues with them being interconnected with any other gear, or A/V systems..
Now, this was only in the 120 volt powered electronic equipment area, so other than newer 240 volt clothes driers having 4 pin power plugs, verses the older 3 conductor type, in which one pin is ground, and the other is neutral outside the normal (2) 240 volt plug`s power pins, and rewiring my brand new SS Mc MC 1201`s to 240v following the factory`s instructions, those amps were grounded @120v, and remained grounded when converted to 240v.. That is the extent of my 240v equipment`s grounding experience..
No hum, or ground loops were present when they were signal connected to the grounded 120v powered A/V rack`s equipment that sent them their audio signals..
Folks, IMHO/E have ground loop problems hooking up gear, usually because they don`t know what their doing, or are indifferent to the rules that apply, this opinion of mine is based on working in the audio field for over 45 yrs.
A good amount of those yrs. involved setting up & running PA`s for rock bands, & my band members equipment & my systems didn`t have ground loop hum, noise issues, or had any shocks touching any powered up, & grounded gear, or each other..
Ground your ungrounded metal chassis equipment, or not, it`s your life, not mine !
Ciao