There's pretty much no way to measure the overall effect because now there won't be a large number of players cut in March by teams trying to avoid paying the players. In the past, there have been several every year.
ADD: As an example, if the Sox added to their pen right now, Brassier gets paid anyways even if the Sox cut him. Seems likely that the overall effect benefits the players.
Long-term implications may be tricky, but the short term is fairly easy to assess (but a lot of grunt work).
1. 2022 (or 2021) salaries of arbitration eligible players who agreed on contracts but were cut before the MLB season then
subtract the 30-45 day pay (where applicable) and then
divide by the total 2022 (or 2021) salaries of arbitration eligible players
= percentage of salary lost to players.
2. 2023 total arbitration estimated salaries (of players who agree with teams),
subtract 2023 agreed upon salaries of arbitration eligible players and
divide that by the 2023 total arbitration estimated salaries (of players who agree with teams)
= percentage of salary lost due to arbitration guarantee rule change.
3. Take the 2nd number and
subtract the 1st number then
multiply the percentage by the 2023 total arbitration estimated salaries (of players who agree with teams) and you get the actual dollars.
If you don't trust MLBTR's estimates you can go back to 2022 (2021), figure out what percentage they were off on the given year, and add/subtract the percentage difference prior to step-3 (this assumes they are consistently off by similar amounts overall).
The REALLY nefarious (or clever) part on the owner's behalf is that these numbers will be used by arbitrators going forward to compare similar players, which can lead to lower Actual arbitration awards (when the team/player can't agree) which could lead to the owners further low-balling players in future arbitration, and so on - endless circle (theoretically). It could also lower free agent contracts as well (due to similar players making lower wages), but it could be argued that the additional available funds increases free agent contracts, so that one is a bit of a mystery.
So, really easy/quick to figure out if you have all of the data in spreadsheets (programs), but if you don't have it already done, the data entry would be rough.