06gsp makes good points, to which I will add the following. Obvious caveat that everything that follows qualifies as IMO.
The two other really important qualities in a progressive commissioner are communication and efficiency.
Re: communication, this applies to everything: setting and explaining league rules, handling conflicts, finding replacement owners, and especially drafts. Communicate early, often, and (in general) decide whether your primary means of communication is sitemail or the league forum, and stick to that. I use the league forum for almost everything, and supplement with sitemail when something important is happening. Again, drafts are the most important part of most progressives, and it drives me crazy when communications are late, sloppy, inconsistent. I probably take this to an extreme, but as soon as the league schedule generates for any given season, I post all of the dates related to the next draft. So two months in advance, owners know (a) when keeper lists are due (b) when keeper lists are finalized (c) when the draft will start, etc.
Also re: communication, be sure to spell out your rules in detail. Few things make me less likely to join a progressive than when the commissioner posts an ad looking for new owners and DOESN'T post the league rules. Or says something like "standard progressive rules." There is no such thing. Every progressive, and every commissioner, deals with dozens of variables differently. How is draft order determined? Reverse order of finish or something else? Is there a lottery for the top pick? What are the criteria for getting in the lottery? Is there a wins floor? By when? Game 120, game 135, game 162? What happens when an owner misses a pick? What happens when an owner forgets to post a keeper? What happens when an owner trades (say) a 4th round pick, and then posts 23 keepers (this is an issue over which there are profound differences of opinion)? What happens when an owner forgets to list a player who is coming back from IR? What happens if the commissioner makes a mistake and includes someone's keeper on the list of available players? There are NO standard answers to these questions, so a good commissioner maintains a detailed constitution where these details and others are spelled out. And if you HAVEN'T done these things, I promise you that there will be conflicts that arise because owners will assume different things about each of these situations.
Re: efficiency, this includes things like really good record keeping on rosters, trades, etc. A best practice is to make sure there is one place (typically a thread in the league forum) where ALL trade details are kept. Including both in-season and off-season trades, and DON'T start a new one each season. I also keep master spreadsheets with every team's roster, and another spreadsheet with all of the available players each season, sorted by position. This makes each season's draft relatively easy to set up and manage.
Lastly, I would not call this necessary, but it definitely separates good from great...how much effort do you want to put into maintaining a league history? Career and single season records, lists of awards, etc. Leagues develop their own sense of culture and community, and one thing that really contributes to a league's identity is its own sense of history.