The fan clutch is a thermostatic device with a viscous fluid coupling, It can fail in two ways 1. Frozen- (always engaged and cooling/ wasting power, you might notice a slight decrease in mpg & power and increased engine noise) 2. Open- the way yours sounds like it failed (Will not properly engage and cool the engine at idle but once you pick up speed enough cool air will pass through the aux fan and through the radiator cooling your engine back down; once you come to a stop light again or idle for a while it will over heat again.)
The way the fan works is counter-intuitive because you would think the fan should be very easy to spin when working properly but not in this case, that's why deleting it can help with engine feel (seems to want to rev easier). To define "some resistance" from my post above, If you give the fan a decent spin (not hard just a normal push) it should want to stop pretty quick 1-2 seconds and you should feel it trying to resist being turned, if it just wants to keep going easily "free wheeling" its shot.
Some thing you can look for visually is any weeping of the viscous fluid as that is also a sign but you might not see anything.
One last thing you can do to check is called the
Newspaper test. Personally i'm not a fan of this method *no pun intended* because i can tell by the way its spins by hand, but a number of people swear by it. Take some newspaper and roll it up into a long narrow tube. *Be careful of your hands/fingers while doing this test!!* With the engine at full operating temperature, take the rolled up paper and insert it on the back side of the fan then move it towards the hub avoiding the blades until close to the hub. Push the paper increasing the friction to the hub area of the fan. If the fan
CAN be stopped with the Rolled up paper your clutch is bad.
As for the price of the O.E fan $200 bucks that's another reason why i would recommend the delete how ever after looking online a little bit i don't see any kits for the e30 only the e36, I did find a forum thread or two where some e30'ers were talking about doing a delete
http://www.r3vlimited.com/board/archive/index.php?t-56144.htmlas far as that goes you will have to do more investigation.
instead of a complete delete you can also look at getting a electric fan that runs off of the battery. It is similar to the complete delete but runs off the battery which eventually means the load is just added to the alternator/charging system but is still much better then the mechanical and i think they are usually cheaper in price, just make sure you get one that can flow enough cfm.