Phone screens were getting bigger before LTE came along. The GSM Galaxy Nexus doesn't support LTE, has a relatively small battery and yet has one of the bigger screens. The Galaxy Note, the phone with the biggest screen, had its initial launch in most of the world without LTE. The 5" Dell Streak before it didn't have LTE either. Nor did the first HTC Titan, the WP with the biggest screen, support LTE.
LTE is strictly a NorthAMerica/Korean phenomena. The rest of the world are buying big screen phones without LTE.