Spell-checkers are so useful, because English is a very difficult language to spell. We have a mixture of several different languages with different spelling rules. More than 90% of English words are foreign. As a comparison, almost all Chinese words are from China. English spelling is based on word history and so English often keeps the foreign spelling!
There are many odd structures leftover from Old English used for only a few words. For example the -ould sound & ending, as in would, should, could is only used in four words. (also bould: an old variation of bold used in the name Bould, a hamlet in Oxfordshire)
Historically English had several spellings for each word. To reform that problem one spelling was often chosen by dictionary writers. Unfortunately the American dictionary writers (such as Webster) and the British (such as Johnson) chose different standard spellings. So we get colour and color. The –or endings were part of an attempt to standardise English, but the British will never let mere colonials tell them how to write the language.
The whole idea of having an alphabet, instead of pictographic characters, is to match the written word to the sound. However in English the written word only matches the sound about 80% of the time. In different places in the UK the words are pronounced differently; then you need to consider overseas varieties of English.
Some countries, France, Germany, Norway, etc... reform their spelling. This can't be done in English, because no authority exists that English speakers can agree on. Dictionaries report what people use and don't rule on what should be used.
We still have to memorise the spelling of all these words. It is difficult for native English speakers who have weekly spelling tests in primary school. It is much more difficult for children learning English in Hong Kong. So having a spell-checker makes school-life and office-life much easier.
The problem with spell-checkers is that when they are overused, we stop learning to spell words. My advice to school children is to try to rewrite the word yourself and not depend on the spell checker. Only use the spell-checker to search for and identify problems. Adults should do the same thing; we must keep learning too.
The other problem is that spell-checkers often correct your spelling to the wrong word. If you have used the wrong word, week instead of weak, the spell checker can't help you. My weekly list of confusing words has examples of these types of very similar words.
Grammar checking by a computer is quite weak. Grammar reflects how we think in a language. Machines don't actually think very well; they only record what we tell them.
Yes, you can catch some mistakes with your spell-checker. But don’t trust it to do a thorough and accurate job. It can help you, but you can't use it to replace learning the language. You still need to reread what you have written.