The key words here are "feasibly possible".
When I was arrested, I would have been thrilled to have access to email; the only phone numbers I could remember were for my
father, who lives out of state, and for my
housemates, who frequently do not answer the phone. I was terrified that I wouldn't be able to get through to anyone before
lockdown. If I'd had access to my email, I could have ensured that someone would find out before morning, but internet access is not available in jail. So instead I got on an indestructible looking telephone made of metal and heavy plastic. It looked like it had been there since before I was born. The cord was too short to use it effectively as a weapon. The sound quality was terrible, and all calls had to be collect, through the
operator, with none of this 1-800 business.
I looked at the phone and thought about the myriad problems of having computer access in jail. Computers are a lot more expensive than phones, and easier to break. That means that if jails get computers, something else doesn't get funded. Computers have a lot more parts that can be used as weapons, glass in the screen, cords, electricity. Most police officers and elected officials are not terribly proficient with computers or the internet, making them unlikely to want prisoners to have access to computers. For those police stations that are encouraging proficiency, prisoner access is likely a low priority. I am also willing to bet that the majority of people arrested do not use email, use it very poorly, or don't know how to access it when they're not at home. In addition, the point of communication from jail is to get someone to come and get you out, so for most people email is not tremendously effective.
To sum up, having email from jail would be cool, but it's still not financially feasible. While the lack of email has probably caused a number of people significant trouble, I would imagine it's a much smaller number of people than had to go hungry due to the jail's failure to meet certain dietary needs.