However if I am starting from a scratch in a language other than Greek, why would I need to retain the accumulated “inconsistencies” and “archaisms” of the Greek original?
It depends on the context.
For an Axion Estin to be chanted at the Divine Liturgy? You probably don't need to retain inconsistencies and archaisms here. Even though this is technically an heirmos to which are sung other troparia (e.g. at the Paraklesis), in practice after Exairetos it effectively serves the same purpose as an idiomelon.
For a through-composed Doxology in the style of Iakovos and later composers? You probably don't need to retain inconsistencies and archaisms here, either. In this context you should focus on proper accentuation as long as you have a sufficient supply of suitable formulae.
For a canon where the troparia of each ode should be as similar to each other as possible to facilitate easy singing and participation? Or a set of slow prosomia (like the ones for the Dormition that we have been discussing)? You might have to retain a few inconsistencies and archaisms here. In this context, a consistent melodic contour needs to be balanced with the constraints of accentuation and phrase division. Striking this balance involves compromise, and this requires an understanding of the evolution of the genre.
For a strophic Doxology in the style of Balasios? You might have to retain even more inconsistencies and archaisms here. In this context, again, preserving the melodic contour from one verse to the next is key, and you may very well have to bend the accentuation rules at times (even in a new language) much as the old composers did.
A simplistic approach like that of the late Fr Papagiannis is untenable. It leads to things like a Kymati Thalassis that is barely recognizable. More generally it reflects a lack of understanding of how the music evolved. Ioannis Arvanitis has demonstrated that there is indeed a logic in the older compositions buried beneath the seeming contradictions and inconsistencies. To create balanced compositions in any language, one needs to understand that logic and be able to apply it when appropriate and necessary, particularly in the slow heirmologic style but also occasionally in the concise heirmologic and new sticheraric.