All for One is this powerful villain, who is almost unstoppable because he has and can use many quirks. Is there any reason why they never used Eraserhead to stop him by blocking all his quirks? Is this just a missing point in the plot or is there any limit to Eraserhead abilities or any quirk to All for One that makes him inmune to Eraserhead abilities?
This is mostly speculation, and incredibly hypothetical. With the evidence given, All For One (A4O) by itself is an activation based or transformation type quirk, and that activation can steal, grant/transfer quirks. However, the quirks that are stolen may or may not be used only when A4O is activated.
Erasure, another "Activation" quirk, can disable the quirk factor of any person caught in range. Thus those with Emitter and Transformation based quirks are disabled, but mutant-type quirks lose their functionality.
As far was we can tell the only time Erasure was used on a person with more than one quirk was on Deku in the skills assessment test (One For All is considered as multi-quirk; the stockpile, and the transfer quirks). However, since Deku only used the "superhuman strength" quirk, we don't know if there were other quirks that have been stockpiled. Also, whether or not a person wielding One For All can use Superhuman Strength + another quirk. This can end in one of two ways.
Conjecture 1: If the root of all quirk based power is rooted in the quirk factor, it is possible for Aizawa to disable A4O and all the stolen quirks with the Erasure Quirk.
Conjecture 2: If the A4O quirk does not need to be activated to use stolen quirks, AND stolen quirks are separate from the Quirk factor of A4O; if and only if each quirk has its own Quirk Factor and Aizawa can disable only one Quirk factor within one person; then A4O will not be disabled by the Erasure Quirk.
Aizawa’s ‘erasure’ quirk works by temporarily disrupting/disabling a person’s quirk factor. With this in mind, there are two possibilities:
All For One’s (from now on I’m calling him ‘The Big Boss’ to avoid confusion between his name and quirk) entire arsenal of quirks could become useless if the quirk factor of All For One controls everything.
If The Big Boss got the quirk factors for each quirk (which seems like the more likely scenario in my opinion), it wouldn’t matter if Aizawa ‘erases’ All For One as The Big Boss would still have dozens, maybe even hundreds of other quirks at his disposal and it would turn into a game of ‘how many quirks can you disable before you have to blink’.
Aizawa is a great hero, but he specialises in close range combat against people who can’t use their quirks. If scenario 2 is correct then Aizawa stands no chance against The Big Boss in a 1v1 however he could be quite useful in an assist role if someone like All Might or Endeavour were also fighting him, he could disable certain quirks before The Big Boss could do any serious damage and maybe slow him down somewhat by restraining/distracting him with his scarf.
It's not explicitly addressed, but during the police preparation before raiding the League of Evil, they make it very clear that they will possibly encounter All For One. Since UA knows All Might's secret, it's not a stretch to also know about All For One.
Logically speaking, if Aizawa could really steal All For One's quirks, he would be absolutely essential to the mission and there would be no reason not to include him... Unless they know that it would not work.
Based on that, while the explanation is not provided, it seems logical that for some hidden reason or another, UA knows that Aizawa won't be able to steal all of All For One's quirks. My guess is that he would only be able to disable the ability to steal other people's quirks, or maybe just one of his quirks - but not all.
According to the anime all for one is a quirk that can take and use quirks, and give them. It also says that it is a storage quirk so it means all of all for one's quirks are within his all for one quirk. There for Aizawa can erase all for one's all for one quirk, and all of all for one's other quirks with it.