A lot of those multi-team ODI tournaments in the subcontinent are frankly a waste of time, showing little quality cricket, are often not taken seriously and are no more than a means of promoting little-known or newly-launched brands. The IPL, for all its problems, used famous brands to get sponsorship, but we've never heard of most of the title sponsors of these subcontinental events.
We had long forgotten about Kitply in India, and they sponsored the ODI triangular in Bangladesh involving India and Pakistan. Then an out-of-schedule ODI bilateral between India and Sri Lanka emerged, and only when the first game began did we hear of the title sponsor, one IDBI Fortis Wealthsurance. Then came yet another ODI triangular in SL, which promoted Compaq, once a leading PC manufacturer, now a cheap arm of HP. Then came Karbonn, an indigenous Indian cellphone manufacturer, who were promoted by the India-Sri Lanka ODI series later. Nobody's even heard of these brands, and any team lifting the trophy will only be giving them mileage.
A lof of these events, as mentioned earlier, involve India and Sri Lanka. This has often led to a whole lot of their players getting injured or suffering slumps in form. That doesn't make for quality cricket. Moreover, some international teams, particularly those not in a tour, but only for an ODI triangular, often send weakened teams, which doesn't often help matters, unless those apparently weakened teams prove everyone wrong.
Then there's the financial viability angle- they just want more money out of more matches in bilaterals.