The LCVP or Higgins boat was designed with one primary goal: to land a large number of troops quickly. Therefore it was important that:
- Troops can disembark as quickly as possible
- LCVPs can land right next to each other, maximising the total amount of troops disembarking
- After disembarkation, the craft can then reverse and return for more troops, evacuating the area for more LCVPs to land more troops
Given this, the solution, inspired by observations of Japan's Daihatsu-class, was to install a large bow ramp so the passengers (which could be jeeps) quickly disembarked from the front into shallow water, but the rest of the craft was still in deep enough water to be able to drive back out.
So why not use rear exits, especially since it's a common feature of modern IFVs like BMP, Merkava or Bradley? The difference is that the LCVP isn't amphibious; disembarking from its rear means troops could end up in deep water and potentially drown in full combat load which made them sink, while not giving them a great firing position and also blocking the LCVP's return trip. With amphibious landers like the BMP, the vehicle can drive onto dry land giving its disembarking passengers great cover.
It's debatable whether having rear exits and forcing troops to swim to the front is better than being able to land more troops simultaneously and overwhelm defenders, but what happened at Omaha beach is the result of multiple failures, and a situation where the LCVP's design simply wouldn't have made much difference either way.