Two coins isn't the same thing mathematically.
If heads = 1 and tails = 2 then:
1+1=2
1+2=3
2+1=3
2+2=4
Average is 3, and the lowest is 2.
D4:
1
2
3
4
Average is 2.5, and the lowest result is 1.
d8/2 (rounded up):
1/2=1
2/2=1
3/2=2
4/2=2
5/2=3
6/2=3
7/2=4
8/2=4
Average is 2.5, and the lowest result is 1.
That lines up mathematically.