Even though Russian does drop the "to be" in present tense for all pronouns, other Slavic languages do feature it either as a separate word or together. For example this is how you say "I am Russian" and "You are Russian" in:
Slovenian:
Jaz sem Rus
Ti si Rus
Croatian:
Ja sam Rus
Ti si Rus
Slovak:
Som Rus
Ty si Rus
Whereas in Polish is a joint word (but the to be is still merged in there):
Jestem z Rosji
Jesteś Rosjaninem
I also thought that using the Latin alphabet feels a bit of a hack and Cyrillic would be a more "natural" way to put things. However, using Cyrillic would impose a higher learning curve for those who do not it.
This is mostly for phonemes that don't have a 1-to-1 representation in the Latin alphabet, like ш, щ, ж and what not. For these cases, languages like Croatian, Slovenian and others have come up with, what is my personal opinion, are quite acceptable workarounds (I just found out that this is called Gaj's Latin alphabet [1])
č, ć, dž, đ, š, ž (I skipped a few).
Without knowing initially how they are pronounced, read in context you do get an idea of what the target sound is.
I also think that on-boarding Cyrillic-first cultures would be easier because normally countries that use Cyrillic as their main alphabet also teach the Latin alphabet at school (Russia for example does and they also teach you how to write "Russian" using Latin characters because they understand the importance of this). Whereas it's not the same way around: a lot of the Slavic countries do not teach the Cyrillic alphabet at school.
> I've always had trouble trying to parse out Russian transliterated into Latin script.
I also think this is because when you're learning Russian as a non-native speaker, the courses focus mainly on Cyrillic (naturally so) so you never really learn that
ж -> zsh
ш -> sh
щ -> sch
х -> kh
ь -> '
etc.
[1]: https://en.wikipedia.org/wiki/Gaj's_Latin_alphabet
Edit: answer question about Russian transliteration, add missing link and try to fix formatting.