Transformer different resulting current and voltage than expected
If you look at the diagram below (a typical power transformer equivalent circuit), you'll see a red arrow that I have marked. That red arrow indicates that a current will flow into the primary winding even when the secondary is unloaded. That current will make the assumption about the secondary current and primary current relationship flawed: -

The magnetization inductance can be found from the data sheet of your toroid: -

Multiply the turns squared by 87 nH to get the magnetization inductance.
If you have 20 turns then \$L_{MAG} = 34.8\text{ } \mu H\$. How much current will this take - you need to factor that into your calculations. However, at the low end of your stated spectrum (10 kHz), the impedance of 34.8 μH is 2.18 ohms and is really dominant. It becomes less dominant at higher frequencies of course.

From 2 MHz to 10 MHz the amplitude of the secondary current is about
1/3 that of the primary current

That's a decent enough frequency to avoid the magnetization inductance problem so then it boils down to leakage inductance and copper loss. For instance, if the net series copper loss (referred to your secondary) is (say) a couple of Ω, then you will lose a significant ability to drive current into the 1 Ω load resistor. You could try using a load resistor that is bigger of course. Then there's leakage inductance (whose impedance rises with frequency) and, at some point this may become quite dominant.
For instance, if the leakage inductance is about 5% of the magnetization inductance it will have a value of around 1.7 μH. At 2 MHz, this has an impedance of 21.4 Ω. Do you see the problem here?
If we referred the load resistance back to the primary is would be seen as a resistance of: -
$$\left(\frac{20}{3}\right)^2 \cdot 1 \text{ }\Omega = 44 \text{ }\Omega$$
And clearly a leakage impedance of 21.4 Ω is going to have some effect at 2 MHz but, at 10 MHz it is going to dwarf the 44 Ω referred load impedance and radically reduce current in the secondary.