In the Acrobat Reader mobile apps, the Commenting tools (such as Highlight, Strikethrough, Underline, Sticky Notes) are not "sticky". As you have mentioned, you need to select a Commenting tool after each use.
Would you please submit a feature request form?
Here's another way to highlight text.
It still won't make the Commenting tools "sticky". But you don't need to activate the Commenting tool and keep reaching out to the Highlight icon in the bottom toolbar. So some users find it less cumbersome or annoying when adding Highlight/Strikethrough/Underline to a lot of pages in a PDF document.
Thank you for the feedback!