I'm an almost-20 years infant teacher, and I've only seen one under-7yo excluded.
That particular kid? His answer as to why he was behaving like this was just "I like being naughty." Unfortunately his behaviour was impacting on other children who were starting to copy him, and he had to go. He ran out of chances basically. There had to come a point where the plug gets pulled for the sake of the other 29 very small children in the room, who are trying to learn.
What does your son say about his behaviour when he's asked at home? That can be very insightful.
If he doesn't like to lose, what experiences of "losing" are you giving him at home to help build resilience? The dislike of losing is very, very common amongst young children, and tbh, they need to experience it regularly. Always letting them win does them zero favours.
What are the consequences at home for poor behaviour at school? "A talking to" isn't going to cut it. Little kids struggle to apply "mummy is cross" to "my teacher told me off 6 hours ago."
Consequences need to be severe enough to be impactful, but also correlated. You were violent at school? Then sorry, it's straight to bed after tea because I can't trust you not to be violent with the family. You broke something on purpose at school? Then you lose access to a favourite toy at home.
Some of the things you've said about him, make me think of high functioning autism. Unfortunately, that can be hard to diagnose in little kids. Because it's a hard line to see between "he's just a bit weird" to "he's autistic". Lots of little kids are bloody odd, but not necessarily autistic.
All that being said, an exclusion can be the best worst thing that could happen. Because it shows the school can't meet his needs, and it'll encourage the ball to roll into more support.
Also, the whole "he's not like this at home" is pretty meaningless. If he can't function in a compliant way outside of the home, then he needs a lot more intervention.