I know that Multibit gave users full control of their keys, but I don't think it was available in 2010. It probably came out the year after. The choices were indeed slim back then.
That's right,
MultiBit Classic first became available in September 2011, and Electrum also dates from that year. However, if we take into account that such solutions were quite new at the time, it is logical that the first users mostly used the easier option (online wallets), even a few years after such non-custodial wallets existed.
This is also confirmed by the total amount of BTC hacked from Mt. Gox in 2014 (850 000), which means that the trust in such services was very high - but it is unbelievable that this is the case even today - millions of BTC are in custodial crypto wallets.