They are one of my favorite franchises other than the Jays. Probably the 2nd best franchise of all time after the Yankees despite having a market similar in size to Pittsburgh, Cleveland, Tampa, etc. I don't know how much the competitive picks have helped, it sure hasn't helped those other franchises to this level.
They are a great example of "winning breeds winning." They have finished below .500 only once since the year 2000 (they won 79 games in 2007) and only 32 times since 1882.
They used to be the southern and western most franchise so they had a large original fanbase that they've been able to maintain with all the winning. Also, their affiliates are strategically placed (i.e. AAA is in Memphis and they've got a big following there) which gives them more population to draw fans from.
Add it all up and over time they've curated a large, hardcore fanbase that punches well above its market weight and allows them to continuously field competitive payrolls.
They've shown that constantly trying to field competitive teams can be an effective long term strategy and one that the Jays should also try to do as well IMO. It just cultivates a better longterm fanbase than the compete-rebuild-compete strategy does.