If LIQD is able to offer these higher interest rates then why can’t xx Bank?

Banks have an incumbent position and rely on customer inherent inaction, or fear to maintain their status quo. Governments  give banks licenses which enable them to earn high profits whilst passing on the minimum to the savings community who support them. 

Over the last decades banks have increasingly lent out savers funds in the form of mortgages, loans, bonds and other products. This means that they have little incentive to innovate and instead keep interest rates far below the real value of those funds. Instead they focus on offering simple convenience and basic access to current accounts, or lending that works on a mass market basis.