well I will take my downvote away, but I still do not agree with your answer, because I see it from a RAW standpoint (which is not enforced, but... well.)
I think it is clear that OP intended it to be a RAW question. But even if it isn't tagged as such, I may answer under a RAW stand point, unless you can show me where it says that you cannot use the reach property I will stay with my answer
there is a magic item for a floating shield :P ... "You need to qualify for the weapon fully to get the other traits of the weapon." <- is that a rules text?
"Reach. This weapon adds 5 feet to your reach when you attack with it, as well as when determining your reach for opportunity attacks with it (see chapter 9)."
It has to be a melee attack, but we replace that with a spell nonetheless. And it triggers, in case of Polearm Master, when they enter the reach while wielding a glaive, halberd, pike or quarterstaff. (Wielding does not require 2 hands, only attacking does)
the opportunity attack is provoked whether you use it or not. Restrictions seem to be: "You can avoid provoking an opportunity attack by taking the Disengage action. You also don't provoke an opportunity attack when you teleport or when someone or something moves you without using your movement, action, or reaction. For example, you don't provoke an opportunity attack if an explosion hurls you out of a foe's reach or if gravity causes you to fall past an enemy."
The PHB chapter says "You can make an opportunity attack when a hostile creature that you can see moves out of your reach. To make the opportunity attack, you use your reaction to make one melee attack against the provoking creature. The attack occurs right before the creature leaves your reach."
Ok, lets break it up... Warcaster lets you replace any AoO provoked by enemy movement with a spell (action, single target, ...), and you can cast spells when wielding a shield/weapon. Polearm Master makes that enemy provoke an AoO when moving in your reach. - without shield that would mean an enemy moving within 10ft of you, gets an eldritch blast to the face. Thats clear... With shield you would still be able to cast a spell.
What let's you believe that for the enemy to provoke an opportunity attack you need to be able to attack? Warcaster let's you replace this attack of opportunity with a spell. So even though you are unable to perform an attack you can replace the possibility of an attack with a spell. The enemy provokes an AoO whether you can attack or not, AFAIK.
The question is not whether the warlock can attack with the Polearm or not. Your whole answer is based around that. The AoO is triggered, whether you are able to attack or not. Did you read the Warcaster Feat? The last part of your answer looks like you didn't. It allows you to perform somatic components while wearing weapons and/or a shield.
@BESW but what is when question 1 asks about "can I use my reaction in my turn?" and question 2 asks about "can i counterspell a counterspell when I casted a non-cantrip spell?". While the answer of question 1 uses an example of counterspelling a counterspell on a selfcast spell... it is not a duplicate. The question is different and goes deeper (see my answer, it won't work on bonus action spells)
Are "optimization" questions not always kind of "opinion based"? If there is no 'flat upgrade' and the question is about "is this feat better than taking two ability points"? Is this not exactly what that tag is about?
I mean something like a "Math AG" would be for helping others with homework and talking about interesting math stuff not really a class thats why I used the quotation marks
Thanks... I have to do some homework for my "English for natural science" class and the docent wants a brief information of what natural science I study (and why) and how good my English is (and how I learned it)
How do you call a voluntary "class" in school after regular school times to improve on certain stuff which is sometimes not available outside such groups? In german it would be an "Arbeitsgruppe" or "Arbeitsgemeinschaft" like 'Math AG' or 'Computer AG'...
@Miniman I would say the point is to "enjoy" it. I would not say that some (emotional heavy) games or fighting a hard boss 10 times in Dark Souls is 'fun', but the feeling after beating it is very enjoyable.
@ACuriousMind I was a bit overwhelmed, coming from a 1000 inhabitants village with at most 200KBps internet into this city... people every where, everytime... with the right connections there is a group activity almost every day... I love it... especially the 15MBps internet.
@Chemus I've invested about 300 hours in this show... and I would say its my favorite show to watch... even above game of thrones, hannibal, walking dead etc.