Let's assume you have a startup and you want it to be registered in Estonia, paying taxes and using the Estonian banks for financial purposes.
1. With e-Residency you can't enter Estonia, you need a separate business or travel visa [1]
2. At present, it’s still necessary to travel to Estonia in order to apply in person for an Estonian business bank account. [2]
3. Good, fancy and catchy name "e-Residency" is actually an infinite loop of bureaucracy. You can't remotely open a bank account, you need to travel personally to Estonia, and you have a chance that banks will approve your application. But you can't enter Estonia with this "e-Residency" for this to happen.
[1] https://e-resident.gov.ee/faqs/about-e-residency/#coming-to-...
[2] https://medium.com/e-residency-blog/banking-for-e-residents-...
And this is just a little tip of the iceberg, there are a lot of articles about real experience of e-residents of how unfriendly for "e-residents" the banks in Estonia are. And without a bank you can't make your startup work.
Today it's just better with the same level of bureaucracy to open a company in other, more startup-friendly countries that grant a residency and have decent, more digital-friendly banks.
I hope something will change in near future, the main idea of e-residency is actually really amazing.