JY
It is highly unlikely that you will get any agreement in here on this issue. For every pilot who has done their initial IR as ME, there will be someone who has done SE first and then upgraded to ME on a subsequent renewal.
My two cents worth - It is actually easier to fly IF in a high performance single or a basic twin (with both engines operating normally) than it is in a C172/C172RG/PA28 type of aeroplane because the high performance single or basic twin tends to stay where you "put it" (yes, even the FTDK which is neutrally stable in the rolling plane). The difference in cost between training in a Bo/C210 or a Duchess/Semenhole is not much, and the twin time in a highly controlled environment will do your future career prospects no harm at all.
I think most IR tests these days confine engine failures and assymetrics in twins to demonstating one engine failure on TO, one in an approach and an assymetric missed approach.
When I started out it seemed like an engine failed every time you looked sideways - always when your other workload was busiest (ie turning inbound in the NDB Appr). I recall finishing one renewal flying a DME homing on partial panel and one engine. Don't think there was much left that the bastard could shut down!
Do the MEIR.
Dr