All the three key activities of banking, broking and custody can only be fully seamless if your broker is a bank too. But that is not too important. If your broking and custody is seamless and if you load funds via NEFT, RTGS, UPI or an authorized payment gateway, then you are good to go. Remember, many brokers charge you a nominal sum to use the payment gateway, so ideally prefer to use the NEFT / RTGS / UPI method for transferring funds as that is normally free of charge. The more seamless these 3 activities are, the less you have to worry about administrative issues.
There are basically two types of accounts called the 2-in-1 account and the 3-in-1 account. In a 2-in-1 account, only the trading account and the demat account are mapped. This is the kid of account that non-bank brokers offer you. But payment is quite smooth nowadays even if you do not have a banking license. It is a good as seamless. It is only brokers who also have a banking license like ICICI Direct, HDFC Securities, Kotak Securities, and SBI Securities that offer you a totally 3-in-1 account. In all other cases, the account has to be funded by transferring money from your bank account.