Cannot copy work from Illustrator to InDesign in InDesign 2024

There's no reason for copy and paste not to work.

For both InDesign and Illustrator try resetting your preferences - this should work on both and you can find more in depth resources to resetting Illustrator preferences.

Try resetting your preferences:

Windows: Start InDesign, and then press Shift+Ctrl+Alt. Click Yes when asked if you want to delete preference files.
macOS: While pressing Shift+Option+Command+Control, start InDesign. Click Yes when asked if you want to delete preference files.
A dialog will appear asking to delete the InDesign Preferences, select 'Yes' on this dialog.
Further info and instructions here if needed:
https://helpx.adobe.com/in/indesign/kb/indesign-preferences-support-file-locations.html

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If still not working

Reinstalling rarely fixes everything - you can do a complete reinstall using the
Creative Cloud Cleaner Tool https://helpx.adobe.com/creative-cloud/kb/cc-cleaner-tool-installation-problems.html

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Is copy and paste the best workflow? I'd say it's fine in some circumstances and perfectly fine to do so.

But would it be better to save the Illustrator file.

Then in InDesign use File>Place to place the file. 

This creates a link to the file accessible through the Window>Links panel

Just wondering if it might be another way to work for you.