>When modern search became more available, a lot of people said there's no point of rote memorization as you can just do a Google search. That's more or less accepted today.
Au contraire! It is quite wrong and was wrong then too. "Rote memorisation" is a slur for knowledge. Knowledge is still important.
Knowledge is the basis for skill. You can't have skill or understanding without knowledge because knowledge is illustrative (it gives examples) and provides context. You can know abstract facts like "addition is abelian" but that is meaningless if you can't add. You can't actually program if you don't know the building blocks of code. You can't write a C program if you have to look up the function signature of read(2) and write(3) every time you need to use them.
You don't always have access to Google, and its results have declined procipitously in quality in recent years. Someone relying on Google as their knowledge base will be kicking themselves today, I would claim.
It is a bit like saying you don't need to learn how to do arithmetic because of calculators. It misses that learning how to do arithmetic isn't just important for the sake of being able to do it, but for the sake of building a comfort with numbers, building numerical intuition, building a feeling for maths. And it will always be faster to simply know that 6x7 is 42 than to have to look it up. You use those basic arithmetical tasks 100 times every time you rearrange an equation. You have to be able to do them immediately. It is analogous.
Note that I have used illustrative examples. These are useful. Knowledge is more than knowing abstract facts like "knowledge is more than knowing abstract facts". It is about knowing concrete things too, which highlight the boundaries of those abstract facts and illustrate their cores. There is a reason law students learn specific cases and their facts and not just collections of contextless abstract principles of law.
>For instance, I'm not too concerned about my child's ability to write very legibly (most writing is done on computers),
Writing legibly is important for many reasons. Note taking is important and often isn't and can't be done with a computer. It is also part of developing fine motor skills generally.
>spell very well (spell check keeps us professional),
Spell checking can't help with confusables like to/two/too, affect/effect, etc. and getting those wrong is much more embarrassing than writing "embarasing" or "parralel". Learning spelling is also crucial because spelling is an insight into etymology which is the basis of language.
>reading a map to get around (GPS), etc
Reliance on GPS means never building a proper spatial understanding. Many people that rely on GPS (or being driven around by others) never actually learn where anything is. They get lost as soon as they don't have a phone.
>but I think my children will have a different perspective (similar to how I feel about memorizing poetry and languages without garbage collection).
Memorising poetry is a different sort of thing--it is a value judgment not a matter of practicality--but it is valuable in itself. We have robbed generations of children of their heritage by not requiring them to learn their culture.