Expanding what PRR said:
... It also seems to me from my limited experiece that the rectifier into choke is a lot less common (even though it is used in the case here) and instead most power supply designs I've seen go rect -> cap -> L or R right? ...
A cap-input power supply is more common for several reasons.
1. More voltage output for a given PT winding.
Copper costs money, and due to the lower rectified output voltage of a choke-input supply (x0.9 instead of x1.414), a choke-input supply means more turns of copper in the power transformer for the same output voltage, and therefore a more expensive PT. This is more relevant when you're dealing with full-wave (non-bridge) rectifiers, because you're only using half the secondary at any given moment. So you're already paying for "2 windings" compared to a PT resulting in the same d.c. output used with a bridge rectifier (but bridges used to impose their own significant additional costs when tube rectifiers were the only feasible choice).
2. Probably less power output.
An output tube can pass only so much current, so if the supply voltage is lower the overall maximum-possible output power is reduced. Add to this that chokes perform their job best if there is always some minimum current drawn through them, meaning Class B operation (idling near zero current) is not a good fit. Chokes also have a maximum current throughput they can handle before core saturation, so massive current peaks are probably not advisable (also tending to rule out Class B operation). The big argument in favor of a choke-input supply is its good voltage regulation (compared to cap-input), but the irony is a choke-input supply also performs best in a Class A circuit (where current for idle and maximum output power are essentially the same). You'll always get less power output for a given set of output tubes and supply voltage running closer to Class A than Class B, and so designers will likely perceive choke-input power supplies as associated with low efficiency.
3. Cost
µF's at high voltage used to be more expensive than H's of iron-core chokes. That equation reversed a long time ago, and use of multiple (and large) chokes in power supplies declined.
4. Weight
Caps are lighter than chokes; from a weight standpoint, you have to be really motivated to use more & bigger chokes for choke-input supplies. The input choke has to carry all the current that will ever be drawn through it under maximum output conditions, and so the core needs to be sized for that plus some reserve to ensure it doesn't saturate and fall out of regulation. That means a lot of weight! I used to have a tube-regulated power supply which could deliver 450vdc @ 200-250mA in which the high voltage was developed in a choke-input supply before regulation. It had multiple chokes and multiple PT's (for high voltage, intermediate voltages for the regulator circuit, filament voltage and bias), and the whole unit weighed over 90lbs! The 10H input choke was easily bigger than a 100w output transformer.
So bigger, heavier, more expensive and all for less output power... No wonder they're not that common. But look at the first post: the 6L6's are being run with 360v plate and 270v screen. The designer needed a way to generate a screen voltage with was not a convenient fraction of the plate voltage (like 1/2, as seen in 6550 amps with 600v plate, 300v screen), and needed good regulation of the screen voltage to prevent constricted output as the amp was pushed to maximum power. The screens also tend to draw reasonably low and steady current (except during brief blips at maximum power peaks, which can probably be supplied by the cap), so a half-wave choke-input supply is a good solution.