Long term impact - the job agency has been around for at least the 16 years I've been on this site. High paying jobs have been around for years. Any impact from the job agency would have been felt way before now. Adding a convenience button changes very little about how the job agency functions. It takes me 1 second now to collect income instead of 1 minute. Not having a mass collect button didn't deter me from collecting income daily. Adding a mass collect button doesn't send alarm bells in my head to remember to collect every day.
"Minimal effort" is a subjective term. I would consider questing every day to be minimal effort. All I have to do is buy items and sell it back to the quest givers to make 3+mil every day without even having to sell the item rewards. Compare that to training your pets- setting alerts to train at every opportunity if I don't want to spend CSC, battling if I want to gain stats quicker, reading books and then being forced to wait x amount of days for the next raise - I'd say that's a hell of a lot more effort up front to get to an end goal when I can readily collect from quests daily. I could play games in the game room and win just as much without investing more than my free time.
You're also making a lot of assumptions about the kind of jobs people want and the kind of effort they want to put into the job agency. Not everyone wants their pet to be a felon. My sheeta is perfectly happy being a master key turner instead of making bank at SAI. Please don't take away his job and crush his dreams of tinkering just because he has the potential to do more with his life.
I have three new pets. After 40 days plus the expense of training stats, one will earn 5,500sP as Shinwa's Scribe. The other two will forever earn the grand sum of 300sP a day because I want them to be the members of a cleaning crew. I don't think the extra income will be bad for the economy just because there is now a collect all button which saves me time getting the wages.
These days I usually only quest if the weekend bonus quest is a good one, I haven't done battle quests in forever, and I would only collect income for my working pets every once in a while. Putting aside the physical discomfort for some people, all that damned clicking is just so time consuming and repetitive. People have other things they need and/or want to do in their limited free time in any given day. I appreciate just one of these tasks being made simpler.
Multiple users were able to collect that much each day by collecting pet wages manually. As for inflation, what items do you think will be inflated? Ordinary quest items? Experienced questers know the range of sP individual quest givers award - if a quest is too expensive and will result in a loss, questers quit the quest.
The Criminal job line was introduced in September 2021 so players who wanted pets in the top position will have done it and collected their sP manually before the collect all button was introduced.
In the old days, R99 items were hideously expensive in player shops which is why players bought the Lizard Minion Trap and Lizard Minion Repellent to use together. It's hardly worth buying these items now because R99s are only a fraction of what they were once worth and it would take years to earn the cost of the Trap and Spray back when the Lizard Minion events are very rare.
Higher tier scrolls and weapons won from battling were hideously expensive when they first came out but a lot of them have come down in price now because battlers won spares to sell.
CSC is something that has really gone up in sP price since Custom Wearables came in. Being able to get CSC from the Bathhouse Pool and Morty Cards has helped a lot.
So, how will collecting all pet wages at once cause inflation and what items will have inflated prices when the Criminal job line isn't new and the highest paying jobs have been around for many years?
I installed an extension on my browser so that I could open all the tabs to collect wages for my 127 pets at once. The 'collect all' button pretty much just makes it so my computer doesn't get upset when I collect their earnings because it no longer has to open over 100 tabs in one go. I forget about jobs sometimes when I'm less active, but I've still collected all their wages plenty of times.
I've always thought of pet jobs as a nice way for pet people to earn back a little of the sP they put into their pets, since we put so much time and sP into them. Getting pets to the point they have decent-paying jobs is a time and sP commitment, and I don't think it's fair to take it away out of fear of inflation when pet jobs have already existed for so long and it was already very possible to collect all of their income daily.

Another thing I'm wondering is how having more than one Mastermind Incorporated pet would be abusing the system. Is having more than one T13 battle pet abusing the system?
Bank interest was bad for the economy because a lot of players hoarded their sP for the interest and rarely spent any of their riches. Even without bank interest many players eventually had so much sP from questing and restocking that various ways of creating sP sinks were introduced. The Hustler came in useful here selling Fanciful Boxes but even the ones costing 9,000,000,000 sP are out of stock now.