I think it has more to do with the dislike of Trump. It Clinton had won, they would be turning on her. Independents didn't want either one to begin with. Before the election 54% of all independents viewed both candidates very negatively or unfavorably. So they were never Trump's to begin with. It's true Trump won the independent vote 46-42 over Clinton with 12% voting third party. But that didn't mean indies like Trump, they just disliked Clinton a bit more than Trump. Still that vote was pretty even.
Independents have turned on Trump, that is certain. Back at the end of January, independents approved of Trump by a 40-34 margin with 26% unsure or undecided. Today using RCP averages it is 36% of indies still approve of Trump, 48% disapprove with 15% still unsure or undecided. But disapproval of Trump doesn't mean independents look upon the Democratic Party any more favorably than they do the Republican Party.
Only 21% of all independents view the Democratic Party favorably, 55% unfavorable. Indies view of the Republican Party is almost identical, 21% favorable, 56% unfavorable.
Yes, the share of the electorate identifying themselves is growing. Back in 2012 according to Gallup 35% of the electorate affiliated themselves with the Democratic Party, 30% with the Republican Party while 35% said they were independents. Today, the numbers are 28% identifying with the Democratic Party, 25% with the Republican Party with 44% calling themselves independents.
Most independents are sick and tired of both major parties. Perhaps that is why we have a four fold increase last November who voted third party over the norm.