The car key just isn't a toy and definitely not for kids (there is then just very small step for them to try driving "a big car" on their own...)

Actually why not ?

When the kid is a toddler, there is no risk of him getting into the "big car" without the parent's knowledge. There is no reason for the parents to get worried about him playing with the keys, if he somehow reached them, other than the possibility of the car getting and staying unlocked outside. This is not a problem if the car is inside the garage, or if the keys are by far out of RF range of the car (when the family visiting somewhere away from home and did not take the car, but took the bundle of keys)

When the kid is bigger kid capable to walk to the car by himself, he is supposed to allready know that starting the big car is forbidden. Safer (and more likely to succeed..) than trying to keep the keys out of his reach at all times, and besides, i would allow and trust him to use the keys to open the car if he wants (such as to get a CD/toy/whatever in or out of it)

But here comes another case, no kid involved. You throw the keys into the bottom of a backpack, throw in some other stuff too over the keys - esp things like notebook computer, and go for a walk. There is just the chance that the laptop will hit the key with its corner, releasing the switch momentarily every time the backpack is shaked up with your steps

it is becoming not that difficult to find an unlocking sequence just by a brute force (the number of combinations to check is then rather limited to few 100's - quite easy task for present computers)

Are the sequences really so predictable ("00000001", "00000002", ...) and not hash-ed in any way with a unique id embedded in the key and car ? This would allready prevent the brute force option (within likely achievable time), even when everybody knows the "internal" counter position

And even without it, what is the problem of setting the start point for the key/car at a random point of the sequence at the time of manufacture (unique to each car), so that allready when the car is shipped it is not too close to "00000001" ?

There is just no free meal. If you want the convenience of a remote key, you should take care of it. The downsize of that is, the key isn't anymore just a piece of metal and plastic, but an electronic device.
So if you trust your child to do only what he is supposed to, it should be not that difficult to explain to him he should not play with the buttons. And if he is not capable of that, he just should not get the keys into his hands.

Anyway letting the keys drop under some notebook or so, there is quite high risk of damaging either the keys or the notebook. Don't forget the key blade is designed to break when exceeding some bending force. The reason is safety of your keys, when you get pushed forward in case of some even low speed collision (the key is supposed to snap before it punctured your knee). But that makes it a bit fragile so even a plastic notebook could easily break it even with small hit (you put the bag with these on a table, whhile the keys happen to be between the notebook and the table). The folding blade makes it more robust, but once the notebook unfolds it (that release button usually needs way less force than the electrical ones), the key remains in it's vulnerable state.
And this snap off is practically mandatory, as no other concept allows both easy access to the key, as well as the safety (well, just the keyless one)

Anyway there is always a way to resynchronize it, but for that either the key has to be authenticated in the immobilizer (or when done via the diagnostic for a key authorized only to open the car, some valid key has to be in the "ignition")

And for the code sequence:
Well, if you know the algorythm how the codes are generated, you know exactly the sequyence.
Each key has it's unique ID, which get encrypted by the pseudorandom sequence, but that is generated by the same algorythm in every car using the same key or car manufacturer. This sequence remains unkmnown, but only until the firmware code leaks out. And that should be anticipated to happen, sooner or later. The longer the technology is in use, more chance it has leaked out. The key ID is generate by a real random generator (involving e.g. real time or so), so even with perfectly known software, you just can not get it except somehow reading it from the key itself.
That ID is known by the key and obviously by the car.
When you want to open the car without the real key:
The ID you obviously do not know initially. But the pseudorandom part you know - except the state of the sequence (how far it progressed).
The latest was assumed as very strong, as the number of openings differ a lot. Wedll, till someone scratched his head and came to a discovery, than it is true only if the car is some time in use. But if the car is new, the number of accesses just can not be that high, so there is just not so many steps to try out.

But once the sequence is really randomly shuffled (and that could be done securely only when two way communication is in place - that is when it communicates with the immobilizer during the engine start authentication), even the generator state becomes unknown, so the hacking method does not work anymore. And this shuffling can then easily made to serve well as the recovery mechanism (after someone toying with the key or so)

I'm happy to stick with old technology. neither of my vehicles have alarms, my car does have lock and unlock buttons on the key fob, and my pickup has no power locks or anything to begin with.

Thankfully I live in a rural area and haven't really had to concerned with the security of cars, most of the time at home and were i work the keys get left in the ignition.

It will be interesting to see how well all the electronic "bells and whistles" on newer cars hold up over time. On some older cars it seems like the overcomplicated electronic and digital type controls can be plagued with issues, although some seen to do just fine.