First, you should revisit that "don't time the market" advice. First, understand where it came from. Stock brokers have a problem: they are supposed to watch the market and advise their customers, but if they make a mistake, they don't want the customer coming back around and saying "well, well, you told me wrong and you should be responsible for my losses". They also want to take the little people's money anytime they walk in the door, and not turn them away merely because market prices are not favorable right now. For business reasons they must have you believe it's always a good time to buy stocks. So they create this meme of "you can't time the market".
I don't have anything against trading strategies or doctrines, but they're not a suicide pact. You shouldn't follow the doctrine beyond reason, i.e. When facts on the ground are telling you something totally different. The first law of investing is Buy low, sell high, and that trumps every other strategy or doctrine.
If CNN has gone into 24-hour-coverage mode about the tanking of the stock market, and brokers are jumping out of windows, then go look at fundamentals. Did they also tank? If the fundamentals are still solid and the stock is underpriced because of panic, then it is low and you buy.
Brokers don't want to be financially responsible for telling you to do that, and don't want to deter you from investing at other times, so they won't tell you to do that. But are they doing that? Are their bosses doing that? Are investment bankers doing that? *Oh you betcha... that's who the buyers are, when ignorant sellers panic and sell low. If they really believed "don't time the market", then they wouldn't be doing that kind of opportunistic investing, would they? :)
So yes. When Wall Street is having a half-off sale, you certainly should be flipping over couch cushions to invest money that you wouldn't otherwise have invested.
So I hope I have disabused you of the notion that timing the market is "ooga booga" bad.
Rebalancing is the best and surest way to time the market
And back to, "this is what the pros do with their own and with institutional money". Rebalancing is gold-plate strategy for endowments, for instance, which are supervised by the smartest investment bankers in the world, as part of their role on university boards.
And back to the laws of investing, you are absolutely correct: rebalancing means you buy low when low stock prices have shrunk its fraction of your portfolio, and you sell high when high stock prices have made them an outsize proportion of your portfolio.
And you are correct that "buy low, sell high" stands in direct contradiction to "don't time the market". Both can't be correct at once. "Buy low" is correct, "don't time" is wrong.