If I have understood the question correctly, there is unfortunately nothing to "solve" here. This is the manufacturer's decision that certain printer models are very cheap to buy, but on the one hand the original cartridges are required and on the other hand a cartridge subscription is a prerequisite for this model, for example. Unfortunately, neither the dealer nor the user can do anything about this. If you do not want a plan, you would have to choose the HP models without an "e" at the end, such as the following:
HP Smart Tank 5105
HP OfficeJet Pro 8024