I agree the IC7000 is no more sensitive to voltage than any other radio I've tested. If you're having problems then it's most likely in your power wiring.
By the way, Icom got screwed by a vendor who provided substandard fuse holders. Quite often simply cleaning the fuses will fix the problem temporarily.
The real solution is to replace the fuse holders. Also If your cable run is more than 4 feet I usually recommend running four 8 AWG power wires. Two for the positive and two for negative lead. I splice them down at the fuse holder pigtails which I replaced with ATM fuses.
The other thing to watch out for is cheap Chinese fuses. Make sure you are using true high quality ATC fuses. many Chinese manufacturers label ATO fuses as ATC. Even Bussman is starting to ship cheap Chinese fuses under their brand name so be careful You're better off sticking with good fuses from reputable vendors such as NTE, In a pinch, you can find really high-quality fuses at a good Marine chandlery but expect to pay more.
I use my IC7000 portable all the time and have no problem maintaining 100 watts output off a 100 amp hour AGM battery. I usually get two good day's calling CQ off a 100 amp hour AGM battery
On my last camping trip, I logged over 350 phone contacts in two days off a 100 amp hour AGM battery on a single charge. Towards the end of the second day, I was still managing 90-95 watts.
Of course, my camping setup has taken IR2 squared losses into account in the design. Since the IC7000 has a remote head I've built special battery boxes which house the battery in one compartment and the radio body mounted in a custom built quick release bracket in the second compartment.
The power leads are 8awg and are just 15 inches long. The battery feeds several large capacitors which prevent voltage drops on voice peaks. I have two such battery boxes. I also have a small generator and a 40 amp 3 stage marine battery charger to charge one of the battery boxes while I operate off the second one.
The battery charger will recharge an 80 percent depleted 100 amp hour AGM battery in about 2.5 - 3 hours so basically, I can operate for 4 days before I need to charge a battery. In practice, if I plan on being active on battery power for more than two days I will only take the batteries down to about 50 percent before swapping and charging.
The batteries weigh close to 70 pounds each so the battery boxes are self-powered with large electric motor driven wheels and an old electric RC car remote control. I used to fly remote control helicopters so this was a fun easy project to build. I'm lazy and have back problems as such I have no intention of man handling 70-pound batteries. I'm thinking about adding telemetry and a camera to the boxes so I can drive them back to the truck or charging location from the operating position. The motors are very strong and easily able to climb motorcycle ramps into the back of my truck.
Since I've built the original battery boxes I've acquired two more identical 100 amp hour AGM's. So I'm thinking about building new boxes to accommodate two batteries each. I've also acquired a second 40 amp charger so I might mount them permanently to the battery boxes.
The chargers I use are the original Statpower Trucharge 40's. these were made for Statpower by Astron, they are Astron SBC-40's, I also have two Astron SBC20's and two of their 10 amp chargers. If you can find one of of the Statpoower 10 amp chargers similar to the SBC10s grab it they are excellent and worth every penny they are super quiet and produce almost zero RFI. Statpower has since been bought by Xantrex and their new chargers are built in China and are the very epitome of junk.
I've discovered it's much easier to operate the IC700 from a picnic bench when the remote head is removed from the body. I have several styles of cell phone car mounts which I use to mount the IC7000 remote head. My favorite has a very large spring clamp on the bottom and a flexible gooseneck which allows me to angle the remote head for easy access. I used to build aquariums so I have skills with plexiglass fabrication So I have also built several stands for the remote head which incorporates a speaker and a remote 7-inch display along with the IC7000 remote head angled to be easily seen while sitting on a table, there's also a detachable sun shield. At some point, if there's enough interest I might start offering these for sale.
The bottom line is if you are operating on battery power keep the battery leads as short as possible and use the largest wire and best fuses and fuse holders you can find.
Of course, the other option is to use a 24 volt DC to DC converter to provide a stable 13,8 volts, the problem here is that I haven't found a single DC to Dc converter or for that matter switching power supply that didn't produce RFI.
Now you might not notice this RFI at your home QTH considering that most residential areas don't have a low enough ambient RF noise floor to see it. For you appliance operators what this means, if you have a constant S5 noise floor you'll never see the S3 RF hash from your inverter, DC to DC converter or switching power supply. That all changes the moment you go camping someplace with a low noise floor.