Doubtful, you still need to convert to AC to transform power to high enough voltages for transmission. Transformers only work in AC after all. There are ways to convert DC power to a higher voltage, like the boost converter, but those aren't really applicable at the kinds of voltages you need for power transmission, 100kV to 800kV... Far too high for any solid state converters.

So if we have to use a transformer to raise the voltage for transmission and then convert to DC, it won't make a difference if we have to feed it AC as the supply anyway. I don't think it will ever become a drawback, just maybe DC power generation will become as advantageous as AC is now.

AC power is incredibly convenient and has served us well for decades, its only drawback really is that you need to sync AC transmission systems so that they're in phase. That is something HVDC transmission does address, but aside from that, power generation in AC is likely to still be more convenient, if only for local distribution.