Yes the resistance increases in the ways you suggested but the current is directly linked to the energy barrer for flipping spins, so it cannot be reduced freely, since this barrier must be high enough thermally. So voltage cannot be reduced freely either.
The same current goes through transistor and MRAM in series. Before there was no MRAM, but comparable current levels through the transistor. But reducing the voltage on the MRAM indeed reduces the sensing margin.
I believe that if the voltage is decreased, then the signal will also weaken.
For example, consider an MTJ with a low "on" resistance of 100 kohm and a high "off" resistance of 200 kohms and it is placed in series with another static 100 kohm resistor. Then we apply 3V across this MTJ and the 100kohm resistor in series. The voltage drop across the 100 kohm resistor when the MTJ is "on" (100kohm) is 1.5V. The voltage drop across the 100 kohm resistor when the MTJ is "off" (200kohm) is 1.0V.
So the "delta V" of the MTJ on off states when measured across the static resistor is 0.5V.
If we had only applied 2V instead of 3, then the "delta V" drops to 0.33 and so forth.
0.5V at nanosecond scale times is kind of the minimum voltage range for modern day DRAM sense amplifiers to work properly.
Correct, it is true that MRAM's high/low resistance ratio not very good (only about 100% I think) which makes it somewhat uninteresting for low power reading. However since it is a non volatile memory, there doesn't need to be any voltage or current applied to it until reading and writing and thus no leakage current for just "sitting there," unlike SRAM where the transistors are holding back a voltage even during non operation and source drain tunneling current is a cause of power loss.
I think the absolute resistance is dependent on the area of the Magnetic tunnel junction as well. For example a 1 um by 1 um junction may be 300 ohm low and 600 ohm high, but if shrunk to sub 50nm, it could be a lot higher. You can also adjust the MgO or insulator thickness of the MTJ to increase/decrease resistance too I think.
MRAM is definitely not without flaws, but it does seem to have hope.