Can a POA limit visitors?

This is a very sticky one. Just because you have POA does not give you permission to limit those who can't and those who can. The main purpose of a POA is to handle financial issues including the principle being sued or to sue in the principle's stead.
IF you attempt to stop someone, especially a family member, you have opened the door for them to take you to Court and have you removed as POA. Why? They will force you to prove whether or not you have done your legal fiduciary duties in Court.
If you are the Court appointed Guardian you can provide a list of those who can or can't, BUT you need a logical reason should you be taken to Court.
I have a list of good and bad. If the bad come to visit, the wonderful staff know I have family members who are vultures circling to make sure there is a piece of pie for them. They can visit but there are limitations. For example, I have a niece who I would not have any guilt kicking her into her next life. Why? She left a voice mail (back when one had those tiny tapes) using such vulgar language all because her mother (my sister) received the Mother's Day card sent to our Mom in my handwriting as 'return to sender' as per Mom's instruction to me. Mom was out of town and I was taking care of her bills etc. Big issues between Mom and my sister. I told Mom that if this spawn ever walks into the house while I'm there, it will be the last time as well as my sister. Who lets their child speak to 1. their Mother 2. their Grandmother like a sailor on leave?
This sister can visit alone, not her husband, the niece ONLY if my sister is with her. Sister's son, NOT EVER!
If they were to even try and take me to Court, I have way too much to show the Court that this sister and her spawn aren't worth the time of day. I have every right as Guardian to protect our Mother from any thing that would damage her mentally as she has Alzheimer's. That is my SWORN oath to the Court and my Mom, even though she doesn't know what is happening in her life.
I am the Mom and Mom is now the child under the Guardianship.

I think if the POA is aware that a particular person/s upset or the principle does not want to see, its the POAs responsibility to keep this person away from the principle. What do u mean by "limit". Not allowing a person visit or limiting how many people visit at one time. If the person suffers from dementia and too many people is overwhelming or even overwhelming period, then I would say yes because its in the best interest to the principle. But to not allowing someone to visit based on the POAs like or dislike is not allowed.

A POA is someone who executes the wishes of the grantor. They don't enforce their wishes on the grantor. So if the grantor wants to see someone, if anything, the POA should help facilitate that not hinder it.

If you want to enforce your wishes on someone, you'll have to seek guardianship.

All I can say is that the two AL's that I have relatives in said that the DPOA cannot stop someone from visiting or taking the resident out. We have an issue with a son of one of the relatives, who is a criminal, the relative has dementia and the son is always conning her out of money, so we are going for guardianship to protect her. With the guardianship we can stop him.

A power of attorney will likely have some power in some circumstances. If there is, say, a disruptive relative who disturbs an elder in the Assisted Living, then the POA will have the ability to act in behalf of the elder for the elders permission. That is one example. Difficult to answer a question with really no details given. Impossible to give a answer that will vary.
For instance. I have a POA. I live alone. There's a knock at my door. It is my choice to answer, to allow visitor in, or to not allow visitor in.
OR
I live with my daughter. She has POA. I have a disruptive Niece who visits me at her home. She doesn't want the niece to come to her house. She has the ability to tell the niece that she is not welcome at her house. Whether she is POA or not.
And so on. All these things usually go according to each case, and the factors involved. Do tell!