Are there other products that have daily options.
I am not familiar with other markets where daily options exist.
Why does only AEX have daily options?
I would say there is limited benefit to having daily options, while there is a certain amount of overhead (cost) with having new options listed.
For each option contract (expiration, strike and call or put) that is listed, the exchange usually has to enlist a market maker or two (or more) who will continuously provide bids and offers for all of the options on that underlying. All of those options have to be updated when the price changes in the underlying market, the data consumes bandwidth on dedicated data links, and the bandwidth costs money.
Each unique position has to be managed for risk and valued, and consumes capacity on the market participants computers as well as the exchange computers.
If these contracts are not heavily traded then market makers will not see any benefit in being more aggressive on the spreads, so spreads will remain wide, so people will tend not to trade them... and so on.
The exchanges have been keen to increase their contract volumes (that's how they get paid) so they have tried various ways to increase the number of contracts with the hope that by having more choices, people will trade more. But what happens is other market participants become skeptical particularly without any obvious additional profit potential, so don't they don't make any extra effort to participate but complain to the exchange about the bandwidth and administrative costs, so that after a few months, the initiative gets abandoned.
In an environment where option volumes are decreasing, exchanges will listen to those who have ideas about how they can get more volume, but many of these ideas tend to fall through. Superficially they sound like a way the exchange can bring in more volume, but the exchanges don't get the buy-in of the market makers to make any real effort.
Market makers now are having a tough time with many closing down completely because they're unable to cover their overhead costs.
We have seen this in the US with:
The dollar strike program. Exchanges experimented with having options with $1.00 price increments between option prices. This is largely abandoned.
Weekly options. The OCC implemented an entire rewrite of the option symbology ("OSI") so they could have arbitrary expiration dates, strikes, but even today there is still much more liquidity in the 'regular' monthly expirations than the weeklies.
Lack of Profit
Also, there is a tendency for the smaller granularity expiration periods only to be used with near-term expirations. For example, it doesn't really matter if an option you buy expires on January 17th 2020, or January 16th 2020, but people are more interested in the next few days.
However, option market makers make their money from premiums (rather than transaction fees) which increase the further you go into the future - options two years out are more expensive than options that expire in the next few days. As a result they would be less willing to trade near-term options as they would make less revenue for the same transaction costs.
There are some mechanisms to create custom options (e.g. flex options) but these are not widely used.
Is there a regulatory reason that only AEX has daily options?
No. Mainly business reasons. Though obviously any new (US) option type has to go through the SRO rule-making process to become effective.