Why is localhost IP 127.0.0.1?

127 is the last network number in a class A network with a subnet mask of 255.0.0.0. 127.0.0.1 is the first assignable address in the subnet. 127.0.0.0 cannot be used because that would be the wire number. But using any other numbers for the host portion should work fine and revert to using 127.0.0.1. You can try it yourself by pinging 127.1.1.1 if you'd like. Why they waited until the last network number to implement this? I don't think it's documented.

Earliest mention I can find regarding 127's assignment as loopback is November 1986 RFC 990 authored by Reynolds and Postel:

The address zero is to be interpreted as meaning "this", as in "this network".

For example, the address 0.0.0.37 could be interpreted as meaning host 37 on this network.

...

The class A network number 127 is assigned the "loopback" function, that is, a datagram sent by a higher level protocol to a network 127 address should loop back inside the host. No datagram "sent" to a network 127 address should ever appear on any network anywhere.

Even as early as September 1981 RFC 790, 0 and 127 were already reserved:

000.rrr.rrr.rrr                 Reserved                     [JBP]
...
127.rrr.rrr.rrr                 Reserved                     [JBP]

0 and 127 were the only reserved Class A networks by 1981. 0 was used for pointing to a specific host, so that left 127 for loopback.

I know this doesn't answer the question, but this is as far back as I could dig. It might have made more sense to choose 1.0.0.0 for loopback but that was already given to BBN Packet Radio Network.

The designers of the Internet really knew how the hardware worked, and they designed with low level implementation in mind.

The values 0, 127 and 255 are special in 8 bit assembly and machine language programming because there are "tricks" you can use to test for these values and branch to different code using smaller instructions that execute faster than for other integers. 127 is the highest signed 8 bit integer, so incrementing it by 1 will cause a signed overflow. Similarly, incrementing 255 will cause unsigned overflow. Merely loading the value 0 into a register will usually set a zero flag on the chip. Imagine the networking program looks like this in pseudocode:

if (value == 0) doLocal();
if (value == 127) doLoopback();
if (value == 255) doNetwork();

Although it depends on the chip, in those days most chips could encode these tests with 2 words, 3 words and 3 words respectively (total 8 words) and further those particular tests were all likely to execute in 1 clock cycle each. Using any other value would probably require 4 words each (total 12 words), a 50% increase in code size and likely a 50% increase in execution time as well.