RS232: To parity or not to parity?

I'm starting to write code for a device that'll stream data in and out in full duplex mode, so I'll be using hardware handshaking and setting a break condition when something goes wrong. But when it comes to error detection it's less clear what the best way to go is. RS232 has built-in parity checking that I could use. As I understand it, if I use 8 data bits, one parity bit and one stop bit then the packet on the wire will be 10 bits. This means that for every 1024 bytes I send, I'm also sending 128 bytes of validation information interleaved with it. Since parity is a 50/50 thing for each byte, it's not too unlikely that a short burst of noise lasting less than one byte will cause corruption that's still consistent with the parity bit. So it doesn't seem a reliable test. If I use a checksum at the end of each 1024 bytes, which is still only 80ms at 115200 baud, my validation overhead goes down from 12% to less than 1%, even if I use a 64 bit checksum. And it's harder to miss corruption. Is parity simply a technology that was useful in the days of sub 100 baud connections and is long since obsolete, and I should go with a block checksum, or am I missing something?