I got acquainted with the polytonic system very young, in primary school, when my mother—a lover of Greek language—insisted that I read children books written in various (polytonic) versions of modern Greek language. At that time (the late eighties) the whole subject seemed strange to me, as in school we were taught a very heavy demotic language and were undergoing the corresponding propaganda.
When in first grade of high school (1994) I learned ancient Greek for the first time, I discovered that the long and short vowels, the accents and breathings, the dative and the nouns and adjectives conjugated in the ancient way, form a coherent system which constitutes the grammar not only of older forms but also of the current form of language. Our written word, “locked” in the system of the official grammar of the Ministry of Education's “demotic”, often uses patterns and types of “katharevousa” so that together they form a single entity, a common current form of Greek language.
I came to the conclusion that the best way to write accurate modern Greek is to investigate all the types and all the systems which have been suggested now and again, and to build one's own system, the one in which one will feel nice and complete.
My own system includes accents and breathings, in a form a bit more consistent with the history of language than the one of Triantafyllidis (although the latter is very good for a first contact with the polytonic system).
For me, the use of a personal linguistic system, built in harmony with reality but not constrained by the official State grammar, is the exercise of the primary right for freedom of expression, which every citizen of a free and democratic society should have. The law cannot constrain our writing into explicit orthographic and grammatical patterns, for any reason whatsoever; and certainly not for the ridiculous reasons which are usually given. Unfortunately both the law which established the monotonic system (1228/1982) as well as the previous laws (on demotic language) and the later ones (on the simplification of historical spelling) are violating that principle, and therefore I can only blame them.
On the other hand, I must admit that these laws are not referring to the way we write our personal texts; they refer to communication of citizens with public services (administration) and to the system thaught in schools (education). But besides the fact that education becomes monolithic and engaged, in reality these laws build an “official” linguistic system, which people who do not really care about this issue consider as “established” and “correct” (!) and not only follow it without second thought, but even dispraise those who prefer something different. In this way, in practice, the power of laws is transferred to everyday life.
Besides that fact, there is no reason why a person wishing to do so should not use the polytonic system. Computers support it in a native way (operating systems, applications and network services use nowadays, more or less, Unicode) and there are many fonts, both free and commercial. As for learning it, this is not a difficult task; whoever wants to learn it can do so by spending a minimal effort; whoever does not, writes monotonically. But nobody should force his/her choices to others.