It seems there are some hikers unaware of the very long tradition of having a register on top of a peak, and they want to get rid of them. On the other hand, many peak registers are very well-hidden, and that may be the case now up on Pusch. I know that for Mt. Kimball there used to be one, but then it became such a popular hike that the register was destroyed. I tried several times to restore it (back in the 90's), but it always got wrecked again by someone, apparently on purpose.
Also, the rise in popularity of geocaching, also known as geotrashing, has made many hikers rightfully very unhappy about seeing yet one more ammo box out there in nature where it doesn't belong.
There are peaks all over Arizona with only a few names in their logbooks. Those are fun to see, because often the signatures go back decades. They are usually well hidden, in a very small jar, under a pile of rocks. I have placed a few myself, in the White Mountains. It's fun to go look to see who has signed them.
Another problem: As peaks have become more popular some newbs think they can use up a whole sheet of paper, write a poem, go on about their miraculous spiritual visions or their ultra-fantastic hiking experience or other drivel that no one else wants to read. The tradition is that you sign your name and the date, possibly adding the name of your town and the name of your hiking club, and brief mention of the weather or other conditions, but not much more than that!! It is considered rude to waste paper in peak registers.
Some people don't care about traditions. I think some traditions are kind of fun to keep going. I see no harm in having peak registers. Educating the public about what they are for is going to be a lost cause, so on extremely popular peaks I think it is better to not have one, or to have it extremely well-hidden, unless there is someone who wants to hike up and maintain it regularly.