I think it depends on whether he is pretending to cook (then yes on the play kitchen) or he just wants to explore, climb, be on your turf (then nope)
They do need to learn HOT, and you dont want them learning that by burning themselves. So when you start heating up something, take your child's hand and hold it over the stove so he can feel the heat. Do it until he understands. (just warm wont be enough perhaps, as he may think "hot" means "feels nice to cold hands" and he'll touch it one of these days.)
Make sure he has a healthy respect for sharp, hot, filled pots on the stove, etc. He absolutely should not touch the dials but I am not sure I agree with turning off the power to the stove (or he'll learn that it's ok to play there, then one day, a real accident will happen because he didnt know that they can and do get hot)
Tot lock some things, but not all. At least one (the one filled with pots, tupperware, etc) should be open and, yes, your dear will make messes, and yes, you will wonder WHY you left that one un-totlocked, but it's GOOD for them. Just make sure it is the one most out of your way (not by/between the stove & sink for example).
When my toddler was pushing our swivel bar stools around to the countertops, that was when they all got loosely tied together, he/we could move them enough to pull out and sit at, but he certainly couldn't pull all 4 to the countertop!
Here in my house, even though my son is past toddler age (but still love to be in the kitchen!) I make sure to have my knives on the far side (ie, a toddler would not reach them if s/he opened and reached in) Spoons are in that first area, then forks next, then knives furthest away.
Pot & pan handles should ALWAYS be turned in. Good habit to ALWAYS have, kids or no! And when things are boiling, cooking, sizzling, you should be there too.
I recommend (on days you have a little bit of patience!) having your son with you in the kitchen when you're there, giving him chores, "teaching" him (at his age, it's all play to you but it's learning to him, by repetition) You've had a lot of great suggestions already on how to incorporate your son and allow him kitchen play, etc. Teach him what he cannot have/touch/do by replacing it with what he CAN. Always be teaching and reminding him what is hot, no he cannot use these knives, etc. (Pampered Chef has a serrated red kids knife - I believe $6 or so? worth it. They can cut like mommy does and not cut themselves.)
I have been in homes where the chairs were all on their sides along the wall, or up on the table, because there was a very active toddler. This phase usually only lasts a few months at most, I believe, only until the toddler has learned how to climb "safely" (or not at all!)