This is not true. I have upgraded my semi annual Super plan, activated using Times Prime, to Premium in previous years. Even now, I have upgraded the Super plan to Super+Ad-free and it also shows upgrade option for premium as you can see from the screenshot below.
Of course not all promotional plans are eligible for upgrade because some of those packs may not be available in Hotstar by default. For example, here BSNL is offering a monthly Super plan which is not available as part of the offerings from Hotstar. You can only buy the super plan in quarterly or annual basis.
These monthly super plans are exclusively designed for partner apps/services. Also monthly Premium plan is not available via mobile app. It can be purchased only via Web. Hence the monthly upgrade option may not be available to him on the app and it shows the annual option.