Chat agent asking bank routing details

I had an agent ask me for my bank routing/checking ID numbers - I
declined asking if agent could email me a link instead of giving them
through chat, which they did.
It should be standard to send a link via email to go through the My
Account where agent cannot have the details instead of through chat.
This is a security issue, possible fraud - routing and bank
information are sensitive.
Is this normal practice? If so, why? It seems like an obvious way to
give someone leeway to clear your account out.

Agent name Shoryakant
chat id-908709084744403344