Monero addresses are quite long. Are there any plans to make them shorter?
No. The 2 keys from which the address is made are 256-bits each, and that's how it is. You can't put 2 cups of water in 1 cup. Not using "hex" but base58 for the encoding already made them shorter, but there's only so many letters in the alphabet. If you used a bigger alphabet it would make them shorter, but probably impractical.
A Monero standard address is 95 characters long. While there no plans to shorten them, OpenAlias (https://openalias.org/) allows mapping a (hopefully much shorter) fully qualified hostname to a Monero address. That is, if you control a domain name, you can setup its DNS record to store Monero (and more) addresses in a secure way using DNSSEC. You then send to mario.magickingdom.com, which is just 22 characters. The software resolves it for you.