(Long and math focused post, sorry)
I have never thought that a d20 was sufficiently random for gaming situations. A 5% chance for perfection and a 5% chance for total failure always seemed too high for me.
I use d100 but process it into the equivalent of a d19(?). Usually you can substitute this for a d20 roll. If low is good you leave it as is and make 19 a disaster. If high is good you add 1 and make 2 the disaster roll.
I'll explain.
When I was first gaming I discovered 1+2+3+4+5+6+7+8+9+10+9+8+7+6+5+4+3+2+1 = 100
That led me to create the following chart
Code:
d100 | d19
----------------
1 1
2-3 2
4-6 3
7-10 4
11-15 5
16-21 6
22-28 7
29-36 8
37-45 9
46-55 10
56-64 11
65-72 12
73-79 13
80-85 14
86-90 15
91-94 16
95-97 17
98-99 18
100 19
Ok here is a graph of how the probability curve you mentioned works with d20s
As you mentioned the chances of a low roll present themselves as being hugely common once you get into multiple dice.
If you switch to my d19 system the chance for a very low roll increases much more gradually.
For example with 5 sets of dice the chance of getting a 4 as the lowest roll is 67.23% using d20 but only 40% using my d19 system.
It might be more math that some people want but if find it shifts the probability nicely.