if you want speed then you shouldn't be using bash and while you're at it avoid using strings (hex) altogether. you are adding a couple of bottlenecks that slow down your process.
instead write your own code and generate random keys based on what you need. you didn't say what you are using it for, so i'll guess it is nothing serious and randomness doesn't matter. for that case you can simply use a fast hash algorithm that produces 256-bit digests and hash numbers from 1 to 1 mil (or whatever message you want) and use the result as the random key. that shouldn't take any more than a  seconds or so.

Remove the ">> privkeys" and pipe the whole thing:
This sends it to "word count" as an example.

This is a terribly slow method for generating private keys though.

keys=60000000; openssl rand $[32*keys] | xd-p-c32

that'll put them in a file named privkeys. replace 100 with 1,000,000 or whatever once you are satisfied it does what you want it to.

btw this may interest you

You can try https://sourceforge.net/projects/pwgen-win/
This is also under Linux
On my pc it can generate 1M keys for 3-4sec, file size 60Mb for 1B will 60Gb  

Can you share what you're trying to accomplish?

Something like https://github.com/matja/bitcoin-tool ?

I'm not sure what would be the most efficient library to generate millions of keys in HEX format (or why you would want HEX format, as you'd lose compression data(?))
But i guess you could also use https://github.com/bitcoinjs/bitcoinjs-lib