The real question isn't who can sign, it's who the bank has to verify
A Power of Attorney is a genuinely useful tool, it lets someone based in India run the account's day-to-day operations while you're abroad. What it can't do is stand in for you at the beneficial-ownership stage of KYC. The bank's obligation is to identify the individual who actually holds 10% or more of the company, verify who they are, and keep that verification current, and that obligation runs to you personally, not to whoever you've authorised to sign.
Video KYC isn't the remote shortcut it sounds like, attestation is
Video-based Customer Identification Process (V-CIP) exists and does cover a company's beneficial owners, but the rules behind it are built for someone sitting in India: the technology has to block connections from non-Indian IP addresses and capture GPS geo-tagging confirming the customer is physically in the country. That makes V-CIP a way to skip a branch visit while you're in India, not a way to complete KYC from your desk abroad.
The route that actually works without travelling is document attestation: your passport and supporting documents attested by the Indian embassy or consulate where you live, a notary public abroad, or an Apostille certificate, all established, accepted paths banks recognise for exactly this situation. On top of whichever route you use, non-resident customers are treated as a high-risk category drawing enhanced due diligence, so expect more documentation and more scrutiny either way, not a quick formality.
What goes wrong without preparing for this
The common pattern: a founder arranges Power of Attorney for a co-founder or relative, assumes the account is now someone else's problem to open, and finds weeks later that the application is stuck at the beneficial-owner and FATCA/CRS stage, the one step only the founder personally can complete. That stall lands at the worst possible time, when the company most needs to move money, pay its first vendor, receive its first customer payment, run its first payroll. Preparing the founder's own documentation alongside the POA, rather than after the account stalls, is what actually avoids the delay.