How is it a fact that the CR system was not designed for that reason? The DMG actually tells you the percentage of EL you should use against a party in an average adventure. The numbers escape me right now, but it was something like 50% should be EL=APL, 30% should be EL=APL+1, 15% should be APL+2 and 5% should be APL+3 or higher.But it is also incontrovertible fact that the CR system was not designed so that every single encounter could have an EL equal to the party's average level.
Seriously...?
I mean, you're clearly aware that not all encounters should have an EL equal to the party's average level. You've even gone so far as to half-heartedly cite some of the relevant passages from the DMG.
And yet you're still asking me how it's a "fact"?
Because, as you yourself point out, even under the strictest interpretation of the rules from the DMG, the CR system was never designed so that all encounters would have an EL equal to the average party level. Period.
The citation you're looking for, BTW, is Table 3-2 on pg. 49 of the DMG.
But to interpret even this table as the "one true way" of encounter design espoused by the DMG is to take it out of context, because on page 48 of the 3.5 DMG we read: "If you decide to use only status quo encounters [...] some of the encounters you place in your adventure setting will be an appropriate challenge for the PCs, but others might not be. For instance, you could decide where the dragon's lair is long before the characters are experienced enough to survive a fight against the dragon." (emphasis added)