Electronic – Is PHY always needed

I see many things that could potentially cause the eye diagram issues that you see. No "smoking gun", but some things that could potentially mess things up.

You have 0.01 uF caps (C211, C212, C214, & C217) on the unused pins of the RJ-45 and the center taps of the transformer. I recommend shorting out those caps. Your use of caps here is unusual and could cause issues later on, although they are unlikely to be causing the eye-diagram issues you're having. Near as I can tell, the only reason to have these caps is as a DC-Blocking scheme for when someone is using a non-standard power over Ethernet scheme. Standard POE doesn't need this protection, and since the POE standard is now "old" you are unlikely to encounter non-POE standard equipment.

Remove C19 and C25, 10 pF caps on the Ethernet termination resistors. These are way too small, and too far away from anything critical to be of any use.

Change C18 and C24, 0.01 uF caps on the Ethernet termination resistors, to at least 0.1 uF. You could even try 4.7 uF. The "power rail" that these caps are decoupling needs to be fairly stable, and there could be a surprising amount of current flowing through the termination resistors. If L4/L5 is restricting current flow too much, and the caps aren't taking up the slack, then you could have data errors.

Remove C16, C17, C22, and C23-- all 10 pF caps on the Ethernet data lines. The only reason for these is EMI filtering and are not needed for debugging. Remove them to make sure they are not causing other issues. You can always put them back later if you need to.

Change C20 and C21, 0.022 uF caps on the transformer center taps, to at least 0.1 uF. 1.0 uF might be good to try as well. This line might be drooping too much given the 10 ohm resistor and L4/L5. You could even short this to VCC for debugging. The only reason for the resistor (and to a lesser extent the cap) is for EMI filtering. When you re-spin the PCB, you should connect the 10 ohm resistors directly to VDD33 instead of going through L4/L5. The 10 ohm resistor and L4/L5 are redundant. By going direct to VDD33 you can prevent injecting noise into your termination resistors and also makes optimizing the filtering in this area easier.

You'll need more caps on the VDDIO pin, or short out the bead. This pin is providing power to lots of I/O pins and will have a lot of current on it. If it is current starved because of the LC filter (bead + 0.4 uF) then you'll have lots of simultaneous switching noise on the I/O pins. That'll actually cause more noise than what you're filtering out with that bead. It's even possible for this noise to make it to the Ethernet outputs.

Verify that you have the pin-outs on your transformer correct. While unlikely, it's possible to have the center tap and another pin swapped. It's worth spending 5 minutes verifying things. For that matter, verify the pin-outs of the LAN8700 as well.

If none of that improves things, then get a 25 MHz metal can oscillator and replace your crystal. I've seen crystal circuits do weird things, so if only for the peace of mind it's worth hacking up your prototype board to make sure your clk is stable.

That's all I see at the moment. Hope this helps!

You need to consider that the data sheets should describe what type of interface is on each device. (i.e. if TX is an output from a particular device or an input). If that is not fully apparent from the data sheet then you should be considering talking to the support folks from the device manufacturers.

I have done designs with RMII both with TX->TX type connection and the crossover TX->RX type connections. It does work.

Another important consideration with MII (and RMII if that is an option that you have to reduce number of inter chip connections) is to carefully consider your reference clock. Ideally you have a clock source that you then route to both devices with equal length routing and very careful attention paid to the signal integrity considerations to keep clocks clean without ringing.

You also want to try to keep the routing of the MII (or RMII) connections with equal length routing for all the signal and control wires.