9 penalties for Palmer (so far) is a lot, but it's not such a freak occurrence as you might think, and he's unusual in that he scored each of the 9 kicks he's taken. Andrew Johnson scored 11 pens in the 04/05 season, Milivojevic, Shearer and Lampard all had seasons with 10 pens scored - can't find the stats for their success rate, but I doubt any of them was at 100% conversion. Bruno in 20/21 and Gerrard in 13/14 also got 9 penalty goals each in a season.
I found a cool table about the number of penalties taken in each Premier League season:
1998-99 | 53 |
1999-2000 | 66 |
2000-01 | 57 |
2001-02 | 52 |
2002-03 | 64 |
2003-04 | 79 |
2004-05 | 74 |
2005-06 | 73 |
2006-07 | 108 |
2007-08 | 82 |
2008-09 | 83 |
2009-10 | 111 |
2010-11 | 101 |
2011-12 | 99 |
2012-13 | 83 |
2013-14 | 87 |
2014-15 | 83 |
2015-16 | 91 |
2016-17 | 106 |
2017-18 | 80 |
2018-19 | 103 |
2019-20 | 92 |
2020-21 | 124 |
2021-22 | 103 |
2022-23 | 98 |
As you can see, it's not a linear trend but the last decade has seen more penalties given than the previous one, and since the introduction of VAR (in Premier League since 19/20) it's been on a steady 90+ a season, with the freaky 20-21 season seeing 124 penalty kicks. So I don't think it's unlikely to happen again that a player takes 9 or more penalties in a season - in fact I full expect this to happen next year. Again, what's mostly unusual about Palmer is the fact he converted 9 out of 9 so far.
Btw, the team to receive the most penalties in a single Premier League season is actually us, when we were awarded 14 pens in the 2019-2020 season.