A few things to keep in mind:
I've only seen a 66 page bill at this point. There seems to be quite a bit of stuff from the GOP talking points missing (sales across state lines, changes to tax credits, etc.). Trump has tweeted that more is coming. At this point I'd say it's not unreal to assume that this is the tip of the iceberg. As such a lot of this in conjecture based on what I've heard may be coming.
That being said the change from the mandate penalty to the continuous coverage penalty is subtle but dramatic. The former says "For each year you don't have insurance you must pay" and the latter says "If you don't have insurance you must pay when you get it." The mandate penalty amounts to negative punishment (if you don't do this thing you will be punished) and the continuous coverage penalty amounts to positive punishment (if you do this thing after waiting you will be punished). While the efficacy of the mandate penalty is certainly debatable it's my personal belief that it will have worked better than the continuous coverage penalty. Let's examine them more closely.
Under the mandate penalty a taxpayer must pay a surtax to the federal government for each month, after a grace period, in which they did not have minimum essential coverage. The surtax was calculated as a percentage of the taxpayer's income and capped at a fixed dollar amount each year. The goal of the individual mandate penalty was to "encourage" younger and healthier people, who might ordinarily eschew health insurance, to enter the risk pool and keep overall premiums in check. In 2016 the surtax was 2.5% of adjusted gross income, capped at $695 per person per year.
Hypothetical scenario: Unmarried male, no children, age 27. Graduated from college, lives in Las Vegas, earns $38,000/year. If this person were to go the entire year without health insurance they would pay a surtax of ($38,000 x 0.025 = $950 > $695) $695. A Catastrophic plan is available off the Exchange for $165.53 per month, or $1,986.36 for the year. While income is below 400%FPL there are no tax credits available because of premium prices in Las Vegas. If we assume that the person does not buy insurance they pay $695 per year, a savings of $1,291.36 per year. And that assumes that they actually pay the $695, which is avoidable if you do your taxes correctly. That same person, faced with a continuous coverage penalty, will absolutely pay nothing for not having insurance. When it eventually comes time to buy insurance he faces a one-time surcharge of 30%. Based on 2016 numbers the surtax is $1,986.36 x 0.3 = $595.91, a one-time charge less than what he would have been paying each year. That leads me to believe that the continuous coverage penalty will lead to more "young invincibles" sitting out coverage, not fewer, which will likely cause premiums to rise.
Then you have to figure in the deterrent effect of the continuous coverage penalty. The mandate penalty goes away when you buy insurance, the continuous coverage penalty is TRIGGERED when you buy insurance. This could very well mean that people who don't buy insurance become less likely to buy with each year that goes by (since premiums go up with age the penalty also goes up with age). Think of it like auto insurance. I know people say to shop around for auto insurance every 6-12 months to get the best deal but there's a catch: that only works for relatively undiscounted premiums. Many (most?) insurers offer huge discounts for longevity plus low incident rate ("3 Year Accident-Free," etc.). They also don't match or carry over longevity with other insurers. So if I have a great discount (30%+) for longevity there's practically no chance that another insurer will be able to beat my rate off the bat. Now, it may be possible that another insurer's base rates are lower than my current rate so that in the long run I would be better off switching and working toward that new 30%+ discount, but it's difficult to make that decision. The same holds true with the continuous coverage penalty. I'm young and healthy and I don't need insurance, and there's no penalty anyway so why bother. Oh, now I'm 30 and the premiums are $200/month plus a $60/month surcharge? I guess I can take care of this infection on my own? Now I'm 35 and premiums are $400/month plus a $80/month surcharge. Well, I guess I'll wait for my knee to heal on its own. 40 years old with $600/month in premiums and surcharge, I guess I'll skip that colonoscopy. It becomes a treadmill of being uninsured that makes the penalty worse the more you need it until at some point the cost of care is going to overwhelm the penalty cost and you purchase, at which point you're going to contribute to a spoiling risk pool and drive overall premiums up even higher.