Further being famously bad at developing software anyone would want to use doesn't necessarily mean that someone is incompetent in all aspects but it would decrease my trust in paypal just a little.
They're similar services when you break them down, but Paypal is almost more like a social network for users, with accounts people may re-use dozens or hundreds of times over a year to pay for things. Many end users probably have no clue what Stripe is and just see a generic Web 3.0-looking credit card form (probably ignoring reassurances about how the merchant website doesn't actually receive the card data; that stuff goes over many people's heads, or they just don't even notice it).
Plus the act of re-entering the credit card number and/or not being able to use a recurring PayPal balance to pay off something might be a non-starter for some.
If I remember right, the older checkouts were hosted on vendor's website -- and you would not know if the cc info really goes to stripe only, or if vendor grabs a copy as well.