So, now you have two problems.
If you're making VOIP calls over a device that is itself connected to mobile networks ... you've still got the connectivity of the device itself to track. Presumably that's a long-lived relationship. At this point the information is limited to location data, but that, at the postal-code level is again sufficient to identify 90% of individuals within the US, based largely on residential and workplace locations.
The notion of having short-lived individually-attributable 5G connection history, perhaps through a dongle- or tether-swapping system, in which many individuals utilise devices for a short period of time, might work. With a sufficient budget, disposable devices might also be an option. (As the cost of SBCs / SOCs falls through $0.10/device, the disposable option might be tractable, leaving SIM card provisioning as the bottleneck.)
The tether is connected over WiFi (the MAC address space is already repetitive, and MAC addresses can be arbitrarily changed at the OS kernel level), giving a two-stage connection to the actual mobile network itself. Frequently-relocating (via a swap) or short-lived / previously unknon tethers, as identified through IMEI is required for mobile connections to work, would still be possible, but at a much greater workload. (I'm very sketch on how 5G identifies specific devices, take what I'm saying here with a few kilos of salt.)
I'd still have concerns with a VOIP device that itself has access to information and computing capabilities, but at least the degree of tracking that's possible over a PSTN direct-dialed mobile handset on a 4G/5G network would be sharply reduced. Other threat vectors remain.
Burner phones on a one-use / short-use cycle would probably be preferable.