The instrument integrates the frequency counter. Similar to that in DG800/900 series, it has the two input couplings, DC and AC. There is at least one confirmed report in the sister thread about the AC coupling issue. When coupling is set to "AC", the center pin of the BNC input connector of the counter is internally tied to -5.3 V voltage level by a high ohm resistor
https://www.eevblog.com/forum/testgear/new-rigol-16-bit-function-generators-dg800900-series/msg3591372/#msg3591372. That seems unusual and I wonder if DG2000 is also affected.
According to Rigol, both DG2000 and DG900 series uses essentially similar HW. But let's look at the frequency counter areas of the DG2000 and DG800 PCBs (attached). The difference is not only in the layouts. In both the designs, the input signal from the connector is first routed to the clamping diode array (a SOT-23 part with JY marking, likely BAV199). Concerning the DC path, the signal is then passes through the resistor of 88 (or 66) Ohm. Then there is a switch that is likely related to the AC/DC coupling. That's where the difference is.
In the DG800, the switch is made of the two SOT-23 parts (with 61U and 6K markings, likely old Fairchild JFETs MMBF5461 and MMBF4392 respectively. Perhaps -5.3 V is a bias voltage for the JFETs, so user must bring his own cap for AC coupling). While in the DG2000, the switch is made of single big part, the marking of which is difficult to read. So the analog front ends are apparently different, and the reason is not clear.
Perhaps it's a minor change because of the parts availability. DG2000 was designed later, and in 2019-2020 both MMBF5461 and MMBF4392 were declared obsolete by OnSemi. While MMBF4392 was replaced with MMBF4392L, no substitution was offered for MMBF5461, so Rigol was forced to change the design. The chances are a later DG800/900 HW revisions were also updated accordingly (pure speculation). That's why it's interesting if the AC coupling issue is related only to the old design or not.
All in all, there is a lot of components in the counter PCB area. Dozens of discrete components and 8 op-amps in total. No idea if every the op-amp is related to the frequency counter, but there is also one 1P8T analog switch (HC4051) the purpose of which is not clear. There is only one that part so it's unlikely it's used elsewhere (as the generator has two channels). It's quite complex electrical arrangement for the frequency counter of unspecified accuracy. Moreover, there is a dedicated 16-bit DAC and two fast comparators. With one more DAC, it could be possible to implement two independent triggers, like in more serious counters, allowing to measure e.g. a pulse edge time. But it seems there are too many stoppers in the SW department.
P.S. JimKnopf, thanks for the hi-res PCB images. Hope you're doing well.