There is no reason why inflation would favor existing members over new ones. Certainly it favors more active members than less active ones, but that has nothing to do with inflation itself. Inflation develues dkp hordes the same as decay. The efficacy of both depends on frequency and magnitude of the adjustments.
For example, if you have players with 10k dkp caches and you want new players to be able to competitively bid on loot within a few weeks, then you just rebalance encounter rewards such that players can earn several thousand dkp per week. The problem with inflation is that you end up working with ever larger numbers, whereas with decay you end up with around the same numbers and a static cap based on encounter volume.
Whether you use decay or inflation, adjustments needn't to be tuned such that monthly accruals are effectively nil within the time frame that you would like been players ro be able to get up to speed, whetther that number is a few weeks or a few months.