If by true phonemic you mean 1:1 relationship between sound and letter, sure; not all the letters sound the same all the time, and not all sounds are always re

If by true phonemic you mean 1:1 relationship between sound and letter, sure; not all the letters sound the same all the time, and not all sounds are always represented by a single letter. It's a natural language so it's bound to have some irregularity. But those exceptions you listed are either rare exceptions (h is always silent, but with a handful of exceptions, normally loanwords like hámster or hachís; x is always "ks" except in old/historical words like México or Quixote), or just follow more or less complex rules. In general if you read and know basic rules, you know how to pronounce 99.9% of the time, if you listen you need to have some deeper level of orthography/etymology/grammar knowledge to write correctly.