I don't know if simplification has broken a great deal of the relationships, but it certainly has broken some.
Here is a specific example:
Traditional Chinese
車禍 [che1 huo4] (car accident)
不過 [bu2 guo4] (however, but)
Simplified Chinese
车祸 (same meaning/pronunciation)
不过 (same meaning/pronunciation)
Notice the 咼 in the Traditional 過 and 禍. This phonetic component gives you some indication that is is pronounced like "luo, huo, guo, wo".
In the Simplified, you lose that relation, because you have the 寸 and 呙 units, respectively.
The phonetic components of Chinese characters don't always give you an exact reading, but they can help you get a good idea of what a character should sound like. There are exceptions, of course.
But even in that case the relationships weren't completely broken. While 过 changed, 娲wa, 祸 huo，涡 wo，窝wo，锅 guo，蜗 wo，etc. still share the radical to the right, and 过 is a very common character, you shouldn't need to guess how to read it.
Here is a specific example:
Notice the 咼 in the Traditional 過 and 禍. This phonetic component gives you some indication that is is pronounced like "luo, huo, guo, wo".In the Simplified, you lose that relation, because you have the 寸 and 呙 units, respectively.
The phonetic components of Chinese characters don't always give you an exact reading, but they can help you get a good idea of what a character should sound like. There are exceptions, of course.