It works, in the sense that yes, your website will be reachable... from everyone having an IPv6 address or going through a network that is able to connect to IPv6 even if IPv4 is used internally.
Technically, configuring both the webserver (and OS) and the DNS for proper IPv6 is now marginally more complex than IPv4 since all major blocks/software is fully IPv6 compatible.
One gotcha you may run into during your tests: since
: is both used inside IPv6 address and potentially in URLs to separate the "hostname" part from the port, there are various places where you need to enclode the IPv6 address in brackets (
So if you see the "half-empty" bottle it immediately means that it will not work 100% of times. Not everyone has an ISP offering IPv6 access (or is it optional, or a separate contract, with separate fees, etc.).
And even further than the ISP, currently IPv6 networks are "less" meshed than IPv4 ones, which means that sometimes there is no route possible between two specific IPv6 providers and there are long standing battles between them. It is rarer currently in IPv4 (or more precisely: it tends to be solved more quickly as the impact is more huge; while in IPv6 it is unfortunately often still below the radar). If you are curious, this is one of the most long running one: https://mailman.nanog.org/pipermail/nanog/2009-October/014017.html
It is true however that some providers do offer IPv6-only hosts for cheaper prices (not because they are altruistic, just because IPv4 is now something scarce, and hence something costly), but that is typically more used for internal servers (databases, back-ends, etc.) that do not need to be publicly faced, and hence can communicate between themselves over purely IPv6.
This is one example: https://news.gandi.net/en/2013/11/IPv6-only-servers/.
Other providers make you pay IPv4 addresses, one by one. So if you use none, you do not pay for them, but you may still have to pay for the webserver/website itself.
IPv6 addresses are not free either: they are distributed the same way as IPv4, RIRs at the worldwide scale distribute them among LIRs which then gives them to various providers. Being LIR has a cost and handling IP blocks for customers is a service, so this has to be accounted for somehow, but the difference is in the space of possible IPv4 addresses vs space of possible IPv6 addresses.
You can find statistics on "IPv6 penetration" at https://www.google.com/intl/en/ipv6/statistics.html for example. But you may wish to put more attention into https://www.google.com/intl/en/ipv6/statistics.html#tab=per-country-ipv6-adoption that shows how things are different per country. And as all statistics, it is important to understand how they are computed because different methodologies can yield different results with not one being better/more right than the other.
Also if you are new in the webhosting/DNS world I would encourage you to try things locally first: your OS should be fully IPv6 compatible, you can install a webserver, configure it, see how things work, etc.
Depending of course at which level you want to operate (just publish a website, or configure it, or maintain a full webserver, etc.), as your question lacks some details.
Alternatively, start with a simple/cheap webhosting solution that has IPv4 and IPv6, look at your access logs to see how people reach your site and if going IPv6 only makes sense (not as easy as it looks like, all the people connecting at some point through IPv4 could be able to reach via IPv6 also, even if normally modern OS and browsers favor IPv6 over IPv4 if there is choice, this is called the "happy eyeballs algorithm")