40 years ago , we just accepted "size matters" and the result was lower bulk resistance at the expense of junction capacitance and bandwidth. gold doping was used to increase current gain and a few other tricks.
But these days Diodes Inc (nee Zetex) hold a huge number of patents for "extremely low" low junction voltages for both Vbe and Vce and they would be my first choice for any power saturated switch. They also have a brand of diodes called **broken link removed**
SBR® (SUPER BARRIER RECTIFIERS)
e.g. ZXTD6717E6 dual complementary SOT23-6
NPN: Vceo =15V; Vce.sat = 0.10 V; I = 1.5A ;
Rce=135 mΩ
PNP: Vceo =-12V; Vce.sat =-0.175V; I = -1.25A;
Rce=150 mΩ
or SOT23 diodes.com/datasheets/ZXT13N50DE6.pdf
Rce=36 mΩ
Putting devices in parallel "can" work ok, if they are matched from the same batch or binned as I get them from my supplier, but thermal runaway can occur when current hogging causes lower diode drops with NTC effect. This can be alleviated by ensuring low thermal resistance substrate heatsink and adding enough ESR in wiring resistance to cover variations in voltage, when used at max current. So essentially the external resistance is on the same order of magnitude as the ESR so that net IR drop is small and "Shockley effect" sensitivity is reduced. I have a rule of thumb for which I have my own design equation that standardizes the required additional resistance for a given ESR , power and thermal resistance for stability against thermal runaway that doesn't require a 2 volt drop with a Constant current source.
Bulk resistance can be modelled as "ESR" in a linear fashion over a useful range of rated current for most diodes including LEDs. There is a direct inverse relationship between ESR and the power handling capability of diodes which depends on both the electrical & thermal resistance and area of the junction.
Then there are another class of diodes they specialize in called Avalanche diodes which are suitable for Laser , LIDAR with absolute max current of 60A in 10ns, all in a tiny SOT23, but have high Vcesat at low currents.