I did not know about ios 9.x not supporting Lovelace cards. Thanks for pointing that out.
Back to the original question. It’s funny that your ‘wishes’ aren’t unreasonable, but I still find they are hard to accomplish in an integrated manner. It really depends on your tolerance. If you don’t mind using the native tablet apps for each task, then you should be fine. But as a kitchen tablet, I’m sure you need it to be hands-free as possible but the technology is just not there yet, unless you can live with limitations.
There are ways to accomplish your requirements, but it’s hard to know what is acceptable to you unless you try it out for yourself.
For music control–do you just need play/pause/next track/play a playlist or you need to be able to browse a playlist for a specific song? If it’s the former, then Home Assistant can do that if you use Spotify. Use the new custom Spotify card for playlist control. Spotify media player integration works great as well.
E-mail - it’s better to just setup the email app on the tablet and get e-mail notifications through the tablet’s notifications bar. If you have a new iPad, you could use the Sideview feature to always show the Mail app, but I think it’'s a waste of screen space.
Recipes - You could create clickable links or a sidebar entry in Home Assistant for any recipe blog sites you visit. Press on it and a web browser would open. Still takes a finger and some time to navigate through the site, search for a recipe, etc. Viewing recipes hands-free on a tablet or smart display is still not very good or easy to do.
On the \homeautomation subreddit, I’ve seen people using the iOS Splitview feature to show two apps together, but compatibility seems pretty bad. I just tested Splitview with Spotify (my main music player) and Plex and it’s not supported. Using Spotify and Plex through a browser works with Splitview, but the interface is terrible. So I know I won’t be using that feature.
The “idle timeout” feature won’t be available on an iPad, unless you find a good kiosk app that can open other apps. An Android or Amazon tablet could probably do it with the “Automate” app.
FYI, if you’re looking into Amazon Fire tablets, those also have outdated Android Webview and will have issues displaying custom Lovelace cards. It’s been like this for at least a year and Amazon refuses to update the Webview component. The only workaround is to use the Google Chrome browser on the tablet, but you get borders around the screen. Fire tablets are also on the sluggish side and will take an extra 1-3 seconds per action vs. an iPad. I just learned to live with my iPad because I like the responsiveness.