Please do not open PDFs in Illustrator unless the PDF was made in Illustrator with Illustrator editing capabilities enabled.
A PDF is NOT a .ai file in disguise, this is only the case if the PDF was made in Illustrator as above.
InDesign’s PDF is a lot different to Illustrator’s PDF – please stop that workflow for your own sake and for the people that pay you to do good work for them.
InDesigns export to EPS is only there as a legacy workflow for systems that have not caught up yet.
InDesign’s export to EPS is intended to be an output only file, meaning that it should never be opened in another program.
Finally, EPS is a much older file system that Adobe is supporting for legacy workflows, you’re much better off with a PDF.
Even so – PDFs should never be opened in Illustrator, unless created in Illustrator and saved with editing abilities for Illustrator.
Basically, if you need a file done in Illustrator then create it in Illustrator. Opening EPS files and PDF files created with InDesign in Illustrator will always be a crapshoot.
Create it in InDesign and export to PDF – no need to open in ILlustrator at all.
Or create it in Illustrator and save it as a .ai file with PDF compatible.