One problem with replacing all the schwas with ə in spelling is it would break the visual relationship between related words. (I don't know if this problem outweighs the benefits that would be gained from otherwise easier-to-learn spelling.)
For example "atom" and "atomic" would be spelled "atəm" and "ətomic". If you're learning the language and you know "atəm" and then see the word "ətomic", you might not know it's related to "atəm".
The situation would be even worse if we decided to spell consonants phonetically. In American English the t in "atom" sounds very different than the t in "atomic". Suppose we introduce a letter ɾ (from IPA) to spell the sound of t in "atom". Then it's even less evident that "aɾəm" and "ətomic" are basically two forms of the same word.
I think it's interesting to consider language as evolving based on the competition of at least four different stakeholders: Writers, Readers, Speakers, and Listeners.
Usually something that seems stupid for one role happens to make things easier for another, like your atom example.
For example "atom" and "atomic" would be spelled "atəm" and "ətomic". If you're learning the language and you know "atəm" and then see the word "ətomic", you might not know it's related to "atəm".
The situation would be even worse if we decided to spell consonants phonetically. In American English the t in "atom" sounds very different than the t in "atomic". Suppose we introduce a letter ɾ (from IPA) to spell the sound of t in "atom". Then it's even less evident that "aɾəm" and "ətomic" are basically two forms of the same word.