Yes the 3 years is a legacy from the pre-July 2012 rules. When my husband applied, we were told he could use either the 3 years spouse route (because he entered the visa system before July 2012) or the five years. He could have still naturalised had our marriage ended but would have to use the 5 years. We went ahead with the 3 year path since you have to have been physically in the UK 3/5 years before your application date, and we had already calculated that he was present here 3 years prior to the application but might not have been 5 years prior.
Yes Meghan can apply for the first LLR immediately after she marries Harry. I am not sure if the Fiancée visa counts towards the 5 years. At one time I know any legal time in the UK counted, even as a tourist, but a lot of things changed in 2012.
Incidentally, there was and is a lot of opposition to the 2012 rules. Basically they were instigated by Theresa May when Home Secretary just to be 'seen to be doing something' about reducing immigration numbers. Most immigration was due to EU citizens moving to the UK, which the government had no power to do anything about, so they decided to go after other groups like spouses. Now people on work visas had somebody to stick up for them, like large employers, universities etc. Spouses had nobody to voice opposition. There were before this about an average of 40,000 family based visas issued per year, which is really a small number since you have to also take into account that some British people also leave the UK to emigrate to their spouse's country, which offsets the 40K.
I do understand the reasons for increasing ILR to 5 years and agree with it. Before, a lot of unscrupulous young men from countries like Turkey and Tunisia (essentially non EU holiday destinations for Brits) would fool gullible older British women into marrying them. They would then leave the British woman the day they got ILR. If you read the British true life stories magazines like Take A Break, for example, there are a lot of those types of stories (the women have often been conned out of money too). Well I'm sure the same thing happens to Americans.
It was thought that increasing ILR would put these predators off. However the new financial requirements were what was most controversial. The British spouse has to be earning at least £18600 per annum (extra if also sponsoring step-children). If you aren't bringing in this amount and want to use savings, you need an incredible £62,500 savings. The big thing in this is lack of flexibility. Relatives cannot pledge to help (in the US they can sign an affidavit of support to help). All they can do is give you £62500, it has to be a gift not a loan. These rules are the second most onerous in the world for spouse visas after Denmark. It has created a lot of 'Skype families' who cannot be together in the UK, made a lot of Brits exiles from their own country, as they have had to move to their spouse's country. And a lot are trapped outside the UK and cannot move back.
Anyway that's largely OT, but it's kind of relevant in that the whole Harry & Meghan saga has re-publicised the situation these families have found themselves in. The financials are of course no problem for our royal couple.