Why can’t the DVD format store FHD 1080p or 720P (given the fact that their storage capacity is more than 4 GB)?

DVDs can store 1080p h.264 videos, you just burn the file to it and view it on any computer or device that supports it.

The DVD Video standard though was made in a time before h.264 and 1080 video was common or even conceived of. Thus the standard format of video that must be supported for a player to be called a “DVD” player is upto 720p video encoded in H.262/MPEG-2.

Many later generation DVD players were able to play DivX or Xvid video but this is not a standard feature or format for DVD Video. The only video disc that can be guaranteed to work in a DVD player is one that is formatted in the standard DVD Video format.

I suspect that Blu-ray in it’s true standard format may not quite fit a full film onto a DVD, but the newer standards might, and they’d require a newer Blu-Ray player to suit. I don’t know if you can have a DVD with the Blu-Ray filesystem and video on it and it be playable as my Google fu is failing today, but it seems kind of pointless when a Blu-ray writer is pretty cheap these days.