There are probably several reasons why this is not the case, but I doubt lack of voice coverage is one of them. AT&T and T-Mobile both use GSM frequencies, but it is reasonably difficult to find phones that use the four frequency bands that they use for 3G coverage.
AT&T and Verizon are both using "700MHz" spectrum. However, Verizon is using the upper-700MHz band and AT&T is using the lower 700MHz band. It is possible (clearly) to support multiple frequency bands, but it isn't free. Plus, AT&T is shipping 700/AWS devices. While Verizon has AWS spectrum, their current crop of devices are 700-only. So, it would mean AT&T supporting three bands 700L, 700U, and AWS.
Beyond that, carriers generally don't do roaming where they have service already. AT&T already has data service everywhere Verizon has LTE. It's slower data service, but it's still service. Voice works the same way. A company might have very low signal in an area, but as long as the phone can get any signal, it will prefer its home carrier. If they had the same policy with LTE, it wouldn't help customers. Heck, Sprint users are allowed to roam onto Verizon for data, but are restricted to 1xRTT (2G) when roaming on Verizon (save for legacy Alltel areas). It might be that Verizon's data roaming rates are so high for newer technologies that it would be unreasonable to offer roaming like that.
Well that's also because nobody's doing voice over LTE, and they're still relying on the legacy network for voice (and fallback data service where LTE isn't available).
Every device sold right now is this hybrid of CDMA/LTE or GSM/LTE, so even if some AT&T device did support Verizon's share of the 700Mhz band on the LTE side, you'd not be able to talk on it on Verizon anyway.
At some point the network will be all-LTE (Verizon's said in the next couple years) and they can drop the legacy hardware. But in the meantime the phones just have an extra bolted-on radio that does a great job at two things: it pulls down data super fast, and it drains the battery just as quick too.