English is a really messy language but there are many simple underlying roots that can tell you what the word means with context clues after hearing it for the first time.
Also learning the International Phonetic Alphabet is probably another huge boon for comprehension, the nicer books often include IPA spelling for crazy off the rip words
However... unless you account that the native speakers and heritage speakers will learn English, making your ability to say cerveza useless. If you aren't fluent and have professional Spanish qualities (like Medical Spanish), its useless. Learning Latin or Greek would have been more useful, at least I could struggle through Cicero in Latin, than saying 3 words in Spanish before the other guy switches to English.
In the US you are very likely, at some point in your life, to encounter native Spanish speakers with poor English competency. Outside of higher education, you are very unlikely to encounter native Mandarin speakers with poor English competency.
The typical student does not emigrate or even travel that much, so you don't prepare them to encounter a human randomly selected from the population of the Earth, you prepare them to encounter a human randomly selected from the regions where they are likely to spend their lives.
I found I already could guess about 2/3 of them from being a recreational reader, but it helped a good deal even so. With the combination of a few years of Spanish and random etymological crawls through Wikipedia, I'm firmly in the top few percentiles of English vocabulary competence.
Edit: I will still say that Greek has little relevance to common English vocabulary, though it is very relevant to almost every scholarly domain. The same is true to some extent for Latin - as the vast majority of non-scholarly Latin words in English are actually borrowed from French, and have (Old) French spelling and pronunciation, not Latin ones.
…I know almost nothing about this topic, but this doesn’t line up with what people who know Latin have told me. They’ve frequently cited the language’s simple grammar as something they like about it.
Because verbs have so many specific forms, it is also pretty common in Latin, as in most modern Romance languages, to omit the subject of a sentence, as it can typically be inferred from context plus the specific verb form - so, you often have to recognize the verb form to be able to understand who the sentence is even talking about (e.g. a sentence might say "amo regem"; if you recognize the words but not the specific forms, this means "love king"; but this unambiguously means "I love the king").
Now, there is quite a bit of regularity here - there are 5 categories of regular verbs (plus some specific irregular verbs), and 5 categories of nouns (though there are multiple sub-categories, as there is some variation in noun forms even in the same category; plus of course some irregular nouns).
Overall no, I don't see any comparison where you could say that Latin is a simple language. All modern Romance languages have universally merged or dropped various of these features. For example, Spanish drops the case system entirely, drops the neuter gender, and reduces the number of moods for verbs.
Wikipedia informs me that Romanian is a Romance language and has retained some of it. Also, the Slavic languages have largely retained most or all of what you’re describing, although they are not classified as Romance languages.
Slavic languages also have a case system (I think it's possible that this is part of why Romanian kept the Latin case system, as there was quite a bit of Slavic influence in Romanian), but they didn't "retain" it from Latin, as they are not Romance languages at all - they simply share this linguistic feature; Latin and Old Slavonic are by no means the only languages with a case system.
Good for getting SAT scores, but 3 years of actual French or Spanish would have done far more for me.