All medical interventions and devices should be free at the point of use, so yes.
While I agree with this, I will note that even in countries with extensive single payer nationalized healthcare, you have to pay for contraceptives (source: live in one)
Ironically, abortion is free here though.
How many abortions happen in Spain relative to the US, would you suppose? Free abortion but not contraceptives would if anything be an incentive for abortion.
I agree that that is if anything a small incentive for abortion though the fact that Spanish women aren't exactly running for abortion as their main contraceptive method probably shows that the amount of people using abortion exclusively for (mainly) contraceptive purposes is fairly small
In any case, the comparison would be, with 2020 data that the US have 14.4 abortions per 1000 women in the 18-44 age range; while Spain has 11.5.
So fairly comparable I suppose, though at the peak of abortion in the US in the 80s and 90s the per capita figure was probably much higher (while for Spain the current data is fairly close to the peak, abortions have been stagnant or even in a very slight decline since the late 2000s)