My husband is ESL, first language Spanish, and I have never noticed he has trouble with articles. His father, who did not learn English until he was in his late 50’s, and his English is still quite broken, does not seem to stumble often on articles, his first language was Hebrew and Arabic, then Spanish; Spanish being his primary language in school and throughout his life. For that matter I don’t think I have a problem knowing where to put an article in Spanish, although I do sometimes fail to know the gender of a word. The one exception is I was taught to use an article when speaking about someone, for instance la JLeslie, my husband’s family never uses that, but an exboyfriend from way back, his Ecuadorian family did.
The point made by @Jeruba, all of those sentences about time, and how each one means something different, that is the biggest complaint I hear from ESL people. In English we have one word mean 10 different things. At least in the examples given about the word time, they all have to do with time, if you know what I mean. My husband tells a story about being in the US and reading a sign, Littering, $50 fine. As far as he knew fine meant ok.
Another thing, my husband’s sister, has horrible punctuation when she writes in English. I mean really bad. I once commented that she is ESL, and my husband said, “it isn’t that, her Spanish is just as bad.” So, possibly, since many Hispanic immigrants are poor in their countries, with little formal education (the average education of Mexian immigrants is 8th grade from what I remember) this might affect their command of the English language, if they speak poorly in Spanish also, not unlike poor grammar in our own ghettos, even if they are third generation American. This kind of marries with @Jeruba statement that she was raised by parents who spoke well, and had strong vocabularies. Although, my SIL did finish high school, did a year of college, and some finishing school in Switzerland. But, that all sounds better than in actual practice, school really was not her thing. But, that is another story. Her spoken English is very good though. As good as my husband’s, who only makes a few consistant mistakes in verb tense mostly.
I also agree with the OP’s explanation as being part of the reason people may have trouble with articles. I disagree with the idea that we text more, use shorthand more. Immigrants have had problems with English even before the computer age. I’m sure it doesn’t help, but I don’t think that is the main reason.