Mage build paths are more complicated than you would think. I'm going to use the example of my favorite mage to explain how mage items work. Also, I'm not speaking for assassin mages like Ahri and Annie. They are assassins, so obviously don't go near that.
Orianna is a utility mage, and as such has the flexibility to either build cdr to support, defense to survive, and raw ap to burst carries in one rotation. BUT she does not effectively build all of these at once.
Firstly, most mages must start with a Morellonomicon. Standard stuff, little deviation here. There are few Ori games where I would consider a different mana item.
The second item is where you make real trade offs. If you want to do as much damage as possible, void staff is the right answer. If you build void staff though, you are giving up hp, resists, and cool down reduction. If your team is behind, you're going to need cool down reduction to provide more shields, cc, and use her ultimate more often. If enemies are diving your team a lot, a Rylai's sceptar can grant you extra peel but you will be sad at how little your damage grew. If you yourself are getting jumped a lot, zhonyas can give your team a chance to save you. Again, a big loss of damage compared to void staff. Luden's bolsters her poking ability and lets her stay in the back of team, and while giving better initial burst for the first 2 seconds, is not as overall strong as a void staff.
Now let's talk deathcap. Mages can not "just build deathcap." Firstly, it costs almost 4000 gold. That's an item and a half, and the build path is not very comfortable apart from the needlessly large rod. If a mage decides to build deathcap, they are committing themselves to putting off their next power spike by quite a bit. Secondly, they are spending gold on raw offense, and are not becoming any better able to survive. Thirdly, deathcap is not worth building until you have about 3 or 4 other items. A raw AP multiplier is not as strong as the MR pen on void staff.
If a mage is able to proceed building like this, either they are fed anyway or nobody on your team is doing the job of just jumping on them because the only stat they have built is AP and that doesn't save you from Zed.
This is a fairly realistic build order that doesn't become fully capable of obliterating an adc until you are near full build. Late game though, almost any carry can 100-0 an adc. This path likely has 100 maybe 150 less AP than the one above, and YES you notice the difference between 550 and 700 ap greatly. It also has fewer bonus AP procs, which are often stronger than building actual AP.