How do people view it all as one pot?
Because if the marriage ended, it would be viewed as one pot, and assigned on the basis of need (particularly for the children's sole residence) rather than according to whose account it was held in. (Obviously a few caveats of upheld pre-nups etc...)
Listen OP, in your situation separate accounts sound sensible. In my marriage a joint account was sensible. (Once we had 3 kids close together, our choice was both of our careers suffer a bit, or DH's career soar and me go freelance, lower my hours a bit, and not work school holidays. Choosing the latter, together, meant sharing his higher earnings or it wouldn't have been fair.)
On a practical level, we had an agreement about roughly how much we could spend on non essentials per month without double checking with the other.
If I remarry, I would need to have a pre-nup to protect the money my late husband left for my needs and then to be passed to our children. As I know that pre-nups are only upheld on divorce if there is more than enough money for everyone's needs to be met from the remainder, I won't marry someone who doesn't own his own home or who isn't sensible with money. (As far as I'd be able to tell - these things can take time to be revealed, I know that.)
I wouldn't necessarily have joint current accounts again. It would depend on a host of factors, but most importantly whether either of us were prejudicing our career for the other.