Rupesh, Your points are valid. I have few SIPs but they are all scheduled on the same date of the month.
I have scheduled NEFT of the total amount on the date of SIP. So in the morning, the amount is transferred to Zerodha via NEFT and same day at 1:30 request for MF is sent to AMC.
Once Zerodha implements STP, you can put lump sum money in a Liquid fund and have to redeemed a day before SIP is scheduled. They have been working on it since long. Not sure when it will be released. Would be interested to know the roadmap of features Zerodha plans to release.