Hmm, I think there are some misunderstandings here about what home education actually involves! It absolutely can be play based, especially for younger children. You do not have to make them "work". You don't have to plan lessons. You don't have to make learning exciting: learning IS exciting, when it is genuine learning which is done because the child has a purpose. If kids are used to having all their time structured for them, it can take a while for them to adjust to finding things to do for themselves, but they will.
Many families do somewhat change their approach as their children reach secondary age, in preparation for GCSEs. Not all families make this change: my two (now 25 and 18) drove their own learning right the way through. Anyway, it's certainly very common to let young children learn by experiencing life. It's good to take them out to interesting places, have good resources at home, read to them, offer them the chance to do projects, and so on, but none of that has to be a chore.
Finances are usually the major obstacle. What would be your plan if your older children went to school? Would you be looking to put the baby in nursery soon so you can return to work, or would you be home with the little one for a few years anyway? If you are going to be at home anyway, you could home educate for those few years and then send them to school when you have to. IMO the key is to meet their current needs as best you can. If they need home ed now, then let them do that now if possible. When/if the time comes that it's no longer viable, they can go to school.
People in the school system often have the view that home ed needs to be a long term commitment, but it doesn't. For a child who suits the school system, moving in and out of school is not a big deal. It gets easier as they get older. Four year olds do take some time to adapt to school, because they are four. Older kids are more capable of meeting the demands of school. They don't find it so hard to sit still and concentrate, or ask the teacher for help when they need it, or wait to use the toilet. My own older child and some of their friends have gone to school at a later age than usual, and found it pretty straightforward. I would say it took my nine year old about two weeks to really get into the school groove, to the point that their classmates and teacher kept forgetting that they'd never been to school before and would say "at your old school...". It's not identical to the journey of a four year old starting school.
On the other hand, for a child who doesn't fit easily into the school system, school is always going to be hard. But wouldn't it be better to let them start off in an environment where they thrive when they are little, and then face the challenges of school when they are more mature, understand their own needs, have self confidence, and have learned some coping strategies? Being thrown in at the deep end does them no favours. A child who is overwhelmed doesn't learn resilience. They learn that they can't succeed, they think it's their own fault, and they come to expect that school can't be a happy place for them.
My older child would have been okay at school or home, and just preferred home education. My younger child has special needs, and I was determined to do everything in my power to delay the time when she had to go into a setting which I knew would have been all wrong for her.