From my experience, most crypto exchanges that prohibit US residents only do so to avoid the hassle of dealing with regulatory nonsense that can result in legal issues and fines. This hurdle can usually be circumvented using a VPN since they are typically only really concerned with the appearance of compliance. Unless you are wanting to deal with fiat, KYC documents usually are not required. That said, some exchanges may require KYC before allowing you to move larger amounts of cryptocurrency in/out, but that usually has more to do with combating criminal activity and compliance for that.
I have found that the pros and cons to trading on a crypto exchange may vary, depending on your goals and which exchange you are trading on. The largest downsides usually involve high fees and/or little-to-no leverage options. Some exchanges do not even allow you to short the market. Liquidity can be a problem, too, depending on what/where you are trading and your position sizes. Trading via a broker seems to solve all of these problems so long as you can trade with decent spreads and ample leverage.
The volatility of crypto is crazy and is like FX on steroids. Because of this, having higher leverage options is not always necessary. Currently, BitMex is probably the best exchange in terms of liquidity and leverage, but the fees can be very high depending on your trading strategy and whether or not you trade using limit orders. BitMex has very few trading options as well, with BTC and ETH probably being the most-traded, which have a 1:100 and 1:50 max leverage, respectively. Binance has many trading pairs and is US-friendly, but has no leverage and no way to short the market. Bitfinex has more options than BitMex, but only offers 1:3 leverage. There are many other exchanges, some offering leverage (usually very low), but are not really worth mentioning here (just my opinion, and I haven’t checked in a while). There are decentralized exchanges, but this is the first one that I have heard of that will offer leverage and possibly, other, non-crypto trading instruments.
Leverage providers for crypto exchanges can be provided by outside investors and/or other traders. I know some traders that allocate extra funds on a regular basis because the interest payments are better than most investments. I believe Bitfinex is around 8%/month, but I am not certain of the details.
Overall, I think that crypto exchanges will need to make many changes in order to compete with the current broker offerings. Trading via a crypto exchange may offer more anonymity, allow you to see the order book and trade 24/7 etc., but the benefits just do not outweigh those of trading via a broker currently (for me, personally). That may change in the future, but I think that it would require much wider adoption first.
I did contact BBOD to inquire about whether or not prohibition of US residents would be heavily-enforced or work on an honor system, and was told that it would be heavily-enforced. The response was given in their public telegram group, so take that for whatever it is worth.