Without Voice-over-LTE, I'm not sure how you're going to get around it. It's not a carrier limitation, it's a limitation of CDMA radios and implementations.
Well, I've often used my mobile internet at the same time as talking in the phone (although it fails sometimes (and I don't have LTE)).
Also, there are many applications in the market that does exactly this. I haven't installed any of them since I basically don't trust anyone with "read/write contacts" and "full internet access" at the same time (perfectly valid permissions for apps like this, but that doesn't mean I trust them).
A search for "vemringde" gives you four apps that targets Sweden specifically (so they are probably quite useless outside of Sweden), one of them mentions that it only works while having a 3G connection.
It's only an issue for non-GSM phones i.e. CDMA phones used in the US and parts of Asia. CDMA does not allow data and voice to run at once over the same radio, while GSM does. Since LTE is an entirely IP network, voice can be run over it like any other IP network. Current phones/carriers do not support it though, but there's some talk that it will be introduced in the next year or so.
Two of the major carriers in the US use CDMA (Verizon and Sprint), while the other two major carriers use GSM (T-Mobile and AT&T). I'm having some trouble finding recent market share numbers for them, but it's mostly half and half.
Not over CDMA without the proper extension that enables simultaneous use of data and voice. And even then, the OS/driver stack has to implement it properly. I can assure you, even on LTE, it does not work on my Android 4.0.4 device.
Also, there are many applications in the market that does exactly this. I haven't installed any of them since I basically don't trust anyone with "read/write contacts" and "full internet access" at the same time (perfectly valid permissions for apps like this, but that doesn't mean I trust them).
A search for "vemringde" gives you four apps that targets Sweden specifically (so they are probably quite useless outside of Sweden), one of them mentions that it only works while having a 3G connection.