With some cryptocurrencies -- such as Monero -- mining is relatively fast and simple and doesn't need a specialized computer to process the transactions.
Mining and 'processing' transactions are different things.
Any older PC can process all transactions happening in the bitcoin network. That's what all Nodes do, miners just as nodes on a 30$ raspberry pi.
On the other hand, Bitcoin is notoriously slow and complex to mine and requires tons of processing power to lift the heavy load.
You could have mined bitcoins with your toaster back in 2009. The process mining itself is pretty straight forward and not complex at all.
You can't mine with your CPU as a solo miner anymore because there is way too much competition. This happened purely due to more people mining bitcoin with better hardware (asics).
But if monero had the same amount of contribution from miner as bitcoin has, you also wouldn't be able to solo mine anymore. It is just a matter of userbase.