I think you missed a crucial point: once the decision was taken to buy PAAMS, & therefore Aster, buying Sylver was virtually inevitable. Aster is not integrated into Mk41. The decision to buy Aster, rather than Standard, may have been related to buying European, but the launcher just followed on from that. The UK would have had to pay for integration & take all the risks. I don't think that was ever considered. The thinking was very simple: you buy whatever launcher goes with the missiles you've decided to buy.
BTW, the price of Sylver in dollars has gone up greatly with the decline of the dollar in the last few years. If Sylver is more expensive now, that does not mean it was more expensive when the decision was made to buy it.
Also, flexibility is valuable only if you want to use it. AFAIK, Type 45 is expected to do air defence, first & foremost. And the flexibility of Mk 41 is often overstated, because people forget that (like Sylver) it comes in different sizes, and only the biggest fires everything. If the choice is 48 Aster 30, or 32 VLS to hold a mix of TLAM, Harpoon, & SM-2, which is best?