The process of paying your company's share capital contribution allows share capital to be paid from any business banking account in the EU/EEA, not just in Estonia, making a bank account in the EU/EEA a great option for some e-residents. This also means that having a bank account in Estonia is not necessary for many e-residents.
Many EU/EEA banks may not be familiar with e-Residency, or location-independent entrepreneurship, but there may be other factors in your favour if you are a citizen of the EU/EEA.
For a start, you are not applying for business banking as a non-resident - the bank is likely to have a better ability to conduct the due diligence necessary to determine whether you are conducting a legitimate business. In addition, you may choose a bank you already have a longstanding relationship with - they will know you much better than an Estonian bank.
A local bank account might also be a better option for you if you are mainly operating your company in your country of residence, you have a large company, your company is involved in manufacturing, or acting as an intermediary to sell the services of others.
Always be sure to provide your banking service provider with as much information about your company as possible to help them understand your business activity. A well-written business plan will help answer any questions the banks may have about your business.