Now give some examples of things you can do with skills that you can't do with perks.
JDR already gave the answer to that. Skills (1-100+) give you fine grained control over exactly how skilled you want to be and you have to plan your skills over multiple levels. Skills determine your success rate at things you attempt i.e. having 50 skill gives you a 50% chance of success for a basic (baseline 0) skill check. Consider the persuasion perk in Fallout 4 - it has 4 levels that are directly tied to the challenge level of the skill checks. In 4 levels you can max it out (assuming you have the charisma). Perks (in Fallout 4) were also tied to the attributes which further reduced character build options. It also forces you to focus on a single thing every character level. Why can't you put points into 2 skills if you want? Or 3?
You also had the ability to "tag" skills to give you the ability to quickly level a small number of skills that were key to your character build. You can't do that with a Perk system.
Consider the trait "Gifted" - which is probably the most popular Trait in F1/2.
Gifted All of your primary stats are increased by one, but you get 5 fewer skill points per level and your secondary skills are lowered by 10%.
Something like this isn't even possible in a Perk only system. You gain less skill every level! A large drawback indeed.
There is also the aspect of player reward. Skills come every level. Perks are something you looked forward to as you only got them every 3/4 levels. The complex builds that the SPECIAL/skill/perk/trait system allowed were one of the strongest aspects of Fallout.
Absolute, obvious nonsense. I played every single Elder Scrolls game on console first and they were the exact same game they were on PC.
What has that got to do with fallout? I was referring to Fallout 4 perks as related to Fallout 1/2/3. I'm also somewhat suprised you playing Arena and Daggerfall on a console
The perk redesign went hand-in-hand with the streamlined User interface design.
Morrowind was usable but clunky on the xbox gamepad compared to the PC. BS had higher aspirations for Oblivion and Skyrim - they need it had to be accessible for the masses (rightly so). That is why the SkyUI and Darnified UI mods are so popular for the ES games. PC gamers weren't satisfied with the UX.
Fallout 3 was a good inbetween design. It works "okay" on both PC and console. It had a consistent looking PIP boy interface inline with the consistent UI in Fallout 1/2. But it wasn't good enough to take Fallout to the next level (like what Skyrim did for ES).
Fallout 4 on the other hand….. The UI has horendous design for the PC (both look and usability). To exit a menu you have to use BOTH the esc and enter keys - ON DIFFERENT sides on the keyboard. FallUI makes a good attempt but it just can't rectify the fundamentally flawed UX that Fallout 4 has for the PC. Fallout 3 stats/perks/skills it was spread over 3 screens - for Fallout 4 it got crammed into a single screen. A screen that was completely disjoined from the standard PIP style (look and feel) interface that Fallout 1-3 used. Mouse and keyboard is a second class citizen compared to gamepad.
The entire problem is that the PC UI is the same as the console version. It has been streamlined for the console. The Perk screen is great for consoles indeed.