I agree with you, that students need Engish-English before they need business English, medical English, legal English ... It takes a longer view than most places are willing to go for. They want instant results for tests and can't spend the time building language competence. They take the short view of lets get down just enough to pass the test, which in the end usually leads to near zero retension a year later and an inability to actually use the language they are memorizing.
I believe that if you are a competent language speaker and competent professional all you need is the vocab. So, I think if you aren't a competent language speaker, that should be your first goal. After all, it's the regular daily conversation that builds good business relations or professional raport. Most meetings or professional situations will be mediated by interpretors anyway. So, it's the ability to converse by the water cooler or at a dinner party that's going to help your company in international business situations.
I teach nursing college students and part-time at a company. Both wanted ESP lessons but I convinced them that a general English conversation textbook would serve them better.
I supplement the textbooks with my own materials to make a connection between what we are learning in the textbook and how that can be applied to medical or business situations. Sometimes I just make reference to how it could be applied. Sometimes I ask them how they could use langauge like what we're studying. Other times, I just alter the conversations a bit on the board.
For example, the first unit for my lowest level medical class is introducing yourself and introducing two people to each other. The text book conversation goes something like this:
A: Sara, this is Tom. He's in our math class.
Tom, this is Sara. She's from Argentina.
B: Hi, Sara. Nice to meet you.
C: Nice to meet you, too, Tom.
I had them change the names to Dr. XYZ and Nurse XYZ. Then add a little information like 'He's from Saku Hospital' or 'He works in cardiology.'
A: Dr. Sanchez, this is Nurse Miller. She's from HE General Hospital.
Nurse Miller, this is Dr. Sanchez. He works in the E.R.
B: Nice to meet you, Dr. Sanchez.
C: Nice to meet you, too, Nurse Miller.
Everyone seems to be happy with that, but I think the key is showing them how that simple langauge that they really need can be applied to the situation they will be in. Then for the students it makes sense to be studying this basic material.
Basic level ESP materials like that might be a good market for materials writers to look to. I know I'd snatch up some remedial ESP medical texts if i could find them.