@jthurstan, there are three different things which might contribute to reading the text. They are the genre, the historical time, and the language.
The genre matters because, as a biblical text, the writers wanted their language to make an impact for generations to come. Therefore, they would want to write things in a constant way, making "This Jesus" a Jesus who still matters to us; "That Jesus" just doesn't sound the same.
Second, the historical time relates. To many of these writers, Jesus' time was just behind them, and some thought that he would come again just as soon. Therefore calling him "This Jesus", again, sets him where he is historical for them, which is recently. At the same time, God talking about "this covenant" is something not even set in a specific historical time, making it relevant for them to place it that way in their own time.
Third, in many languages verbs and tenses do not work the same as in English. In Greek and Hebrew, it is hard to translate a word to being "this will be" rather than "this is". And knowing what we do about the time and the genre, keeping it in a voice of relevance and constancy with the times was very important.
Admittedly, I might be wrong on all counts, this is what I know from my own studies of the bible in school and church, hopefully it is at least moderately helpful.