I find that even with the adjustment proposed in the DMG, the CR system for a single opponent tend to break. Using the spreadsheet, a 'beyond deadly' encounter for 6 4th level PCs is a single CR8 monster. I could pit them against a single Assassin. If he successfully ambush them and does his 7d6 attack +4d6 sneak attack, +6 to hit, he'll probably drop one PC per round of successful attacking (roughly 75% chance). On the other hand he will probably not survive a second round (AC 15, 78 HP against 6 PC... if they realize he can one-shot characters they will go all out). So it's not deadly as in 'is the encounter difficult or memorable?' but as in 'he could one shot us, thankfully he dropped like a fly). And the same could be said for several other monster : either they have area attack that could result in TPK, or are sure to drop in one or two round, which doesn't provide a memorable fight. Deadly, maybe, but not memorable. I find the CR system working better if postulating roughly one foe per PC, but it's not always thematically appropriate. Since, using CR as a guideline can be useful.
One of the other thing I am not sure with CR is how to tweak the system when the PC practice their 5 minute work day... not because they cheese the game like madmen, but because the adventure calls for it (if they are running an investigative adventure where fights are few and they can get a long rest between them, being in a city with a rather lose time pressure. Going for the whole 'daily amount of XP' in a single fight results in overpowered fights (or the PC plowing through low level opponents like the three musketeers did to the cardinal's guards...).