UI remark: the ordering of the elements is not the best imo. Here is what I would do:
Input field
Alias length
Check button
Register using the wallet address checkbox
Register button

This follows the workflow: first check, then register. It also prevents clicking the wrong button by mistake as they are more separated.

A few more UI nits:
Register active wallet address => Register to the active wallet address
The register button could show the registration fee, like "Register alias for 556 XEC".
If this doesn't fit due to space constaints, the fee could be added to the length string "This alias is 8 bytes in length, registration fee is 556 XEC"

• add some space between the alias length and the check button
• the check and register buttons should not look identical. maybe include a magnifying glass ("search") icon on the check button, and a dollar sign or some other appropriate icon on the register button. Also different colors.

In D14713#330683, @emack wrote:

Re-arranged UI per feedback, updated label for active wallet registration checkbox.

The register button could show the registration fee, like "Register alias for 556 XEC".

This was a design decision to not show the price here because it would be an API call per keystroke to get the price for current length. Even though the price is not expected to change frequently we felt it was better to have a single source of truth on the server side, which is called only once at the registration confirmation dialogue. Alternatively I can keep a copy of the pricing array in Cashtab so it can achieve pricing reads on the fly without calling the API but I'll need to manually keep it in sync with any pricing changes on the server.

I thought this was done already ? Or maybe it's only on server side, I can't remember.
You should do an API call on each block and store the value locally, obviously a lookup for each keystroke is the wrong design.