I believe in Purgatory, and like CS Lewis think it's common sense. Otherwise (to use an extreme case) you have the situation of a serial killer, or someone like Adolf Hitler, loaded with bad, cruel and evil habits, making a sincere deathbed confession and then just waltzing into the absolute holiness of heaven, without so much as a "by your leave".
He'd need a bit of cleaning up first.
And of course there is St. Paul's comment about someone escaping "through the flames". There's a sense of someone being heavily singed, like standing too close to a bonfire.
What I do have difficulty with is the business of the souls in Purgatory needing our prayers. For one thing, if someone has been dead for 100 years, and they're still in Purgatory, who is even going to know they're there?
It's one thing to pray for someone you know eg. a friend who died recently, but I wonder about those who are in Purgatory for a period longer than a human lifespan, and who have been forgotten by all those who knew them or knew of them.
I'd have thought the cleansing effect of God's burning fire (or love) would have a far more salutary effect than our prayers. The impression I get is that the request for our prayers shortens the time, but doesn't do the job of cleansing the "holy souls".