What is the usual day schedule for day traders at a futures prop firm? In particular, do they try to make small profits early in the day only to risk these profits and get bigger wins later in the day? This means if they lose their daily allowance they cannot lose more in a day. On the other hand, if they are lucky, they can score some big winning days which would not be possible otherwise.
A first step in developing a consistent trading method would be to excise the word "winning" from your vocabulary. This includes each form: wins winners winning winnings won.... a systematic trader does not win.
I don't know about "prop firms". But I would say the opposite is more likely. The first 2 hours(+/-) of the morning generally, usually, provide a significant portion of a trading days volatility. This time period has a name... the golden hour(s). Traders thrive on volatility. I know several traders that trade ONLY the golden hour(s). The other period of higher volatility, generally, usually, is the last 30 minutes of regular trading hours. Everything else generally, usually, is lunch time somewhere. FWIW, @tommcginnis speaks truth.
Would a plan to trade about 2 hours in the morning in market A, 4 hours in the afternoon in market B and last 2 hours in market C make sense? Each market in a different account - this way there would be 3 "sessions" in one day. Each account with its own loss limit.
If your trade methods(s)/plan(s) have tested satisfactorily (to you) for those markets during the specified times, it may make sense. Personally, I think you are asking and worrying about the wrong things.
Why would they be able to secure a small profit early in the day ? If they can secure a small profit each and every morning then why would they risk it later ? They are wizards in the morning and gambler in the afternoon ?
OK. I will ask a bit differently: if you had 3 markets to trade, one at a different time of day, would you trade each in a different account or in the same account?
There is a place for such an arrangement. But the purpose is different... it is based on the type of trading. For instance a daytrading account, a swing account, and an investment account. It's not about risk, it's about availability of capital. Why would I want to eat into my capital for my bread and butter day trading, with maintenance of a swing position in sugar or a long term position in wheat? Why are you looking to complicate your life? Multiple accounts does not make a trader profitable.
I trade different accounts if the assets are in different currencies. Cryptocurrencies I trade in a different account because I have to. But ideally, I would prefer my general 'at risk' fund to all be in one account and available everywhere. It takes time to shift funds.