Personally I prefer creating WEBI variables for the reasons you already listed - WEBI variables are easier to manipulate, customize, etc. Whenever it is feasible I utilize generic BEx queries with no BEx variables and create WEBI prompts for filtering.
However this approach works for BEx queries returning small to medium size set all possible records. Threshold determining what is small or medium size multi-provider most likely varies from company to company and from your DB technology.
When I tried to create a BEx query on top of multi-provider that is - for lack of better term - gigantic I did not have issue creating BEx query in BEx query designer however I was not able to use this BEx query. Query panel froze for like 20 minutes before I killed the session without even creating Query object. (Not that I wait for 20 minutes every time I create BEx query but for once I was willing to sit patiently and create a WEBI report on top of the generic BEx query I created on top of ginormous multi-provider)
I have done high level performance comparisons in WEBI comparing two identical reports - one with BEx variable as a prompt and another with WEBI parameter as a prompt. If there was a performance difference - it was insignificant. One could assume that without BEx variable as a parameter SAP BW returns all the data back to BO server then BO server applies WEBI prompt filter. However based on my experience I do not think it happens that way. Seems to me that WEBI is smart enough to make a proper MDX call to SAP BW that contains MDX version of SQL "where" statement based on WEBI parameter, thus limiting data that have been returned to BO server.
But one thing I have learned - what works for one multi-provider might not work for another. Each case and each report is different. Occasionally I need to create a report specific BEx query to address performance issues and occasionally I create report specific BEx query to simplify how report is built in WEBI. For example recently I was asked to develop report to measure customer sales performances over different time periods. I started out with generic BEx query but time period calculations required building complex calculations within WEBI. It worked but I re-did report using customized BEx query that utilized CKFs and RKF that were somewhat straight forward compared to complex WEBI variable calculations I had before.