Tritium is made on the large-scale by fissioning Li-6. There is no special requirement for a heavy water reactor. HEU can also be substituted to a degree with Pu-239 in thermonuclear weapons though it's lower critical mass complicates design.
Heavy water reactors produce around twenty times as much tritium per energy output as other types of reactors, so while there isn't a requirement for them it's the best way to optimize output. More information in Table 2 on page 221 of
this book and page 13 of
this document.
Long burnup times which are standard across the board for power reactors means that the Pu-239 from such a route is heavily contaminated with Pu-240. As a short-lived alpha emitter it produces considerable heat which seriously complicates weapon design.
I forgot about that. Unless the reactor is going to constantly go through loading and offloading cycles, the best way to counteract that is with an online refueling system, so the fuel can be taken in and out as required. That means separate fuel tubes too. I don't know if online refueling is possible for a PWR, but it has been done with BWR reactors, and it's common on heavy water and gas cooled designs.
Gas cooled reactors are an awful route for making weapons.
The low thermal capacity of nearly all gases forces you to highly pressurise the gases and run your reactor at very high temperatures. High pressures in tun mean you need a heavily constructed reactor vessel and complicates on-line loading and unloading of the reactor.
Actually, the later series Magnox reactors and all the Advanced Gas Cooled reactors were built with steel reinforced concrete rather than pressure vessels. They don't require complicated equipment to build and are even considered safer than steel vessels.
Heavy water makes up one of the largest capital costs in building a CANDU reactor.
Well, I certainly didn't say it was cheap.
Light-water moderated reactors don't accel at weapons production because they require enriched fuel.
That would seem to be an important caveat. Usually light water is both coolant and moderator, but the RBMK was a water cooled graphite moderated design that seemed to have some features that could lend themselves to weapons production, notably the online refueling capabilities/fuel tubes.
Gas cooling was only really common in the UK in the early years of nuclear power. Not because it was good, but rather pure nationalistic spite as not to be seen copying the Americans.
At high temperatures, gas cooling has nearly all the same drawbacks as water cooling; it operates at very high pressures and the gasses are poor thermal conductors.
It's important to distinguish between the early gas cooled designs in current use and some of the later ones that were tested and that are proposed for future use. The British and French lacked heavy water for heavy water reactors and didn't have much electricity to spare during their economic recovery for light water, so enrichment wasn't a feasible option either. Gas cooling was thus a second best option, as they would only require natural uranium and could reprocess the spent fuel for plutonium. Without the need for extensive enrichment capabilities the military program could supply more electricity to the grid as well.
As you point out, these early gas cooled designs had lower efficiency than even the light water designs. Carbon dioxide isn't the best gas for a nuclear reactor from an efficiency and maintenance point of view, but it's easy to acquire. In addition to that issue, the early gas cooled reactors were Rankine cycle/steam turbine units, so they lost further efficiency by transferring the energy in the gas to water. The water cooled reactors can do that directly.
However, in terms of advanced reactors, a gas cooled design using helium cooling can achieve very high temperatures (hence their name very high temperature reactors) and use the helium to directly drive Brayton cycle gas turbines, a technology first used in natural gas power plants in the 1960s and now very well refined. It's possible to get similar levels of efficiency from steam, but that requires using supercritical steam technology that has only been used in a few coal fired power plants and poses additional challenges for a nuclear unit given the need for higher safety standards.
If you want nuclear weapon material you'd go as simple and as low cost as possible. That means light-water cooled, carbon moderated and natural uranium fueled, running at atmospheric pressure and potentially even open pooled style for easy fuel swapping. You could easily insert tubes filled with either natural lithium or Li-6 into the reactor to produce large quantities of tritium.
The RBMK is supposed to have been a very inexpensive design, so this seems like a possible option as well. I'm only aware with it being used for the RBMK though, so I'm not sure what issues are tied to the technology as opposed to that specific design. Also, it doesn't really explain why other countries went for gas cooling to fill the same role in their early nuclear programs, and my guess for that is the technology probably has low efficiency.