What in particular would they not be allowed to use private money to do?
Would individuals that aren't running be allowed to use private money to do those things?
Also, in the pre-election time mass media have to offer equal conditions for all parties - if you own a TV station and run ads for one party for $1/minute, then you have to offer the same ad slots for the same price to all other parties as well.
I mean, it's not simple and it does require some limitations of what the people and media can do - which might conflict with USA 1st amendment, but in general the problem is somewhat solvable, it's somehow done elsewhere and so you can look at worldwide experience to pick out the bits that work best.
Can I buy a $10k radio ad supporting some particular issue that the candidate also supports?
Can I buy a radio station and hire talk radio hosts that argue in favor of the candidate or issues the candidate supports?
>but in general the problem is somewhat solvable
I think that depends on what you count as "solvable". The systems which address the problem probably work better for some people and less well for others. Which people do you have reason to believe are beneficiaries of these systems, and what reason do you have to believe that?
On the other hand, it has some advantages for the established politicians as well, after all they set the rules for this system - in essence it avoids an arms race. Lifting the limits would give them some advantage over the smaller parties and upstarts, but nothing over their real competition, but that would mean that all the major players would suddenly need to raise many times more money, making everyone more dependent on donors.
Who are the losers in this case? Probably the very wealthiest individuals (not "the 1%" but the top 10-100 richest people), since it limits their influence. At any one point of time one or another party (not necessarily the largest one) may have an advantage in financial support and would be happy to lift or raise limits so that they could buy more votes, but if something like that happens, then it motivates everyone else to not let that happen.
Regarding your questions - it depends, that's more a question for the lawyers. IMHO ads supporting some issue would be fine but talk hosts arguing in favor of some (any) candidate would be prohibited in pre-election campaign time window - e.g. all mass media interviews with candidates during that time would be only in the scheduled slots or as advertising. Sure, if you control important media or people then the limits can and do get bent quite a bit beyond their intent, but it still sets a limit. I mean, if the stated limit is 10 then everybody might push it to 11 by various means, but you can't really do a meaningful large scale money-influence campaign without it being obviously illegal.
In regard to promoting political candidates, what in particular should individuals unaffiliated with the candidate not be allowed to spend their private money on?
For example, should I be allowed to spend my own money to buy a computer which I then use to post comments on message boards which argue in favor of some candidate?
Should I be allowed to spend my own money on a computer which hosts a website which argues in favor of some candidate?
Should I be allowed to buy a newspaper and then selectively hire journalists who I believe are biased in favor of the candidates that I prefer?
