I find it surprising that only in the past few years someone started to use statistical analysis (Markov, bigrams, trigrams) on this script. These are techniques that have been in use by cryptanalists for decades. Sounds like something very basic that you would do in the initial efforts to analyze any ancient script.
Not necessarily. IIRC, people trying to decipher Mayan glyphs with cryptanalytic methods were set on the wrong track and got nowhere, because a script is actually meant to communicate language, not to hide the message.