No way can you change your own oil faster than one of those drive through places. Just going to the store to buy oil and a filter is going to take longer than driving through.
The case of changing oil is that you need a place to utilize it (workshops have a license for that), because you won't drain it to the sewers, will you? So, changing oil yourself is quite pointless.
Not sure where you live but auto part stores in the US accept used oils for recycling free of charge.