No. Do not dissolve political parties. It would defeat the purpose of our bicameral system of government. Don't get rid of the parties, get rid of the corrupt bureaucrats passing themselves off as politicians.
That's not what
bicameral means -- it means we have the House and the Senate. There can be (and are) members of either house that belong to no party.
The downside of having political parties is (a) we have in effect a duopoly featuring two puppets identical except that one wears red and the other blue; and (b) it incites people to think and act in massive blanket statements -- see the application of the term "RINO" where some public official is expected to put party first and constituents second.
And that's where we get equally useless blanket broad-brush blather such as "Republicans are racists" and "Democrats founded the KKK". And as long as that goes on we remain mired in the mud, full of sound and fury, signifying nothing, sniping cheap political points that are effectively meaningless.
And (c) it means that nobody gets elected to a major office without a huge moneyed institution behind them. Genuine people can't compete.