There are a lot of threads like this so you're not alone op.
Personally I don't know why people put up with it! My ex tried it on at start of marriage and I made it very clear that no way was all the chores and household admin gonna fall to me!
With 20 odd years more life experience now and having seen other relationships and how they work on this score I am now of the opinion that it's best to resolve this before moving in together certainly before dc as after that point it gets harder to change as they have you "trapped"
You may find the following links amusing/interesting/helpful
www.huffpost.com/entry/she-divorced-me-i-left-dishes-by-the-sinkb9055288/amp
www.workingmother.com/this-comic-perfectly-explains-mental-load-working-mothers-bear#page-2
m.youtube.com/watch?v=SqQgDwA0BNU
Time for a "come to Jesus" chat with dh to discuss and if he's resistant I see no problem telling him enough is enough, you are one person and cannot do it all yourself and he needs to pull his weight!
Personally I think in extreme cases an absolutely valid reason to leave so don't know why you felt you had to open saying you weren't considering leaving.
It's lazy, disrespectful and selfish!
A strategic strike (not doing anything that only benefits him eg his laundry) might have an effect but really you're 2 adults and parents you should be able to come to a reasonable agreement
Ex and I had an almighty row that led to our discussion. Not the best approach but I was young (22) and lacked confidence to raise difficult discussions which culminated in my reaching an exhausted end of tether moment.
He was at first adamant his way was right and even called mummy for back up - unfortunately for him mummy backed me up!  as did fil!
Then we sat and talked it over and agreed on a chores split that was fair and meant that mostly we could each avoid the chores we loathed and do the ones we hated less and a split of household admin too.
Personally I've found (and again I agree this is unfair/isn't how it should be) that this type of man sometimes is a bit better if they have assigned jobs that are "theirs" that they take ownership of and you're (plural) clear on how often they're to be done (which I won't go into as that WILL start a bun fight on mn!) and don't let his jobs all be the "once a month" 5 minute ones while yours are all daily and hours long!
He's a grown ass adult at heart he KNOWS he is a lazy shit! He's perfectly capable of doing his share
@PlanDeRaccordement idea of splitting if one is a night owl and one a lark makes sense to me - I'm a night owl hopeless in mornings! But very productive at night
Could you do mornings with dc and of an evening he does bath/bedtime, Prep packed lunches in fridge etc? Which would mean less to do of a morning too?
Also - lower standards where possible and accept different people do things different ways. I'm very much "my way is the best way" and had to resist that.
In terms of a reasonable split whatever method you choose it should mean equal down time for each person - no him lounging about while you're still doing chores at 11pm knackered!
Pps are right though the only way he's going to BECOME competent is by actually doing it!
My ex when we first married couldn't cook! Really honestly couldn't. I taught him but really this involved LETTING him make mistakes on occasion and laughing about it! Like the time he thought a "clove of garlic" in a recipe led to him using a whole bulb, or when he was learning to peel carrots and frankly he threw more away than we ate cos of how clumsily he peeled! But he learned and I hear he's a pretty good cook these days
The one thing he never managed was laundry - at least the washing part. At first I got annoyed with him then on a couple of occasions I literally watched him do it and he had done it all correctly and yet somehow there was still shrunk items! I have no idea how! But that was fine I did the laundry and he did the bins and cleaning the kitchen, which I HATED doing.
This WILL impact on dc in a way they notice as they get older and it will impact their views of relationships.
If you have sons they'll expect to be waited on hand and foot seeing as dad does sod all, if you have girls they will likely end up in similar or worse relationships.
Ex and I had couples counselling ages ago (following mc we lost our way a bit as a couple) and the counsellor said the top 3 reasons couples seek counselling are in order: (there was a survey carried out around this time she was referring to)
1 money
2 split of household responsibilities
3 in laws!
I think anyone familiar with mn would agree this isn't really surprising
But I'll admit I was surprised as I expected infidelity to beat out one of those but counsellor said no as people tend to either leave the cheat immediately or decide to ignore and move on.
Bereavement/loss was 5th apparently, 4th was couples facing fertility issues.
If there's to be no consequences for him carrying on as usual he's not gonna change, you have to make it less easy for him to do that really