The short answer: centuries of use of Old Church Slavonic instead of Latin or Romanian as a written language BUT note there is a tendency towards analytic tenses in spoken languages across Europe.
The long answer:
Questions of the form "Why?" in historical linguistics are not necessarily answerable, but we can try.
One theory could be that there was some difference in Vulgar Latin dialects at the time of the split, and there may have been, for that we would need the comparative method.
Another theory is that there was some factor since the split, however we define it, some time in the first millennium.
As we know, the other major Romance languages, and even many of the now minor ones, were essentially in constant contact with written Latin as they evolved from Vulgar Latin. So the orthography and prescriptive grammar of the standard languages have always lagged behind the vernacular languages, and conversely, the standard languages remained an influence on the vernacular.
Notably, Latin was a liturgical language, and a bureaucratic one, and for this reason the lexicon, semantics and grammar in those spheres evolved less. An obvious example is Spanish espíritu, Jesús and Dios, which, if the normal shifts that occurred between Latin to Spanish had been applied, would by now be something like *espirito, *Jeso and *deo, like Romanian zeu.
Another example of continued legacy is the mismatch of orthography and pronunciation in modern French, as extreme as that in English, if more predictable. That only happened because the literary class were continuously writing Latin, then Old French, generally dragging their heels at every step. It would have never happened had the French woken up one morning and decided to write their language for the first time.
Meanwhile, in Dacia:
The oldest surviving written text in Romanian is a letter from late
June 1521, in which Neacșu of Câmpulung wrote to the mayor of
Brașov about an imminent attack of the Turks. It was written using the
Cyrillic alphabet, like most early Romanian writings. The earliest
surviving writing in Latin script was a late 16th-century
Transylvanian text which was written with the Hungarian alphabet
In the 18th century, Transylvanian scholars noted the Latin origin of
Romanian and adapted the Latin alphabet to the Romanian language,
using some orthographic rules from Italian, recognized as Romanian's
closest relative. The Cyrillic alphabet remained in (gradually
decreasing) use until 1860, when Romanian writing was first officially
1521 is very very recent, given that the Roman province of Dacia was founded in 106.
The Romanised Dacians, of course, ended up Christians and as literate as any others over the centuries, the liturgical language, however, was Old Church Slavonic, with a bit of Greek, and the political language was also often Slavic, or even Magyar or Turkic, hence voivoda, cneaz, ban and so on.
Both other Romance languages and Romanian have masses of doublets, borrowings from earlier or parallel branches of Romance in addition to inherited words, but the Romanian ones happened mostly during a sudden and short but massive wave in the late 19th and early 20th century, whereas the borrowing into the other languages was more continuous.
But suddenly prescribing grammar, as opposed to lexicon, is much more difficult, it sort of works if there is continued passive literacy in the standard language, but suddenly introducing new structures top-down sounds hard, and I am not aware of many examples of it. In any case, the nuances of parse trees and morphology do not appeal to political and cultural forces the way that lexicon and pronunciation do.
The result is a language which is both more divergent in some ways with regard to Latin, and more conservative in other ways, especially with regard to Vulgar Latin, in lexicon, and in grammar.
The future tense is notably absent in Romanian, and it's instead constructed with a modal verb vrea (eu voi / tu vei etc.), which makes me feel like I'm looking at a Germanic language.
We can theorise, certainly Romanian is part of the Balkan Sprachbund, but there is also plenty of Romance influence on the non-Romance languages of the Balkans, and, moreover, a tendency towards fewer and more analytic tenses is observable in languages across Europe.
Re-use of to want as a future auxiliary specifically is a feature of Old Church Slavonic, Serbo-Croatian and Bulgarian and Albanian, but in Bulgarian and Albanian it is an indeclinable particle, exactly like o să in Romanian, and it is a feature of Yiddish, and English, but not modern Standard German.
So Romanian mirrors nearly exactly the situation in South Slavic, right down to the incomplete shift to the indeclinable particle, but keeping in mind of course that this is not Slavic per se, as this is not seen in East or West Slavic, so Slavic is not obviously causal here.
https://en.wikipedia.org/wiki/Old_Church_Slavonic_grammar#Future is not very explicit, but https://en.wikipedia.org/wiki/Old_Church_Slavonic#Basis_and_local_influences claims:
Periphrastic compound future tense formed with the auxiliary verb 'хотѣти' (xotěti, "to want"), for example 'хоштѫ писати' (xoštǫ pisati, "I will write").