Question

Is inbreeding really efficient at producing homozygosity?
Let us suppose the character we are trying to establish is dominant trait controlled by a biallelic gene and the two individuals (animals) we have selected to inbreed both have the genotypes Aa.
Aa x Aa = AA/ Aa/ aa in the ratio 1:2:1
So the possibility of having a homozygous dominant is 25% while that of heterozygous is 50%. As the breeder has no access to technologies and find out the genotype of the F1 individuals there's a possibility that he would choose two F1 individuals with Aa genotype once again (which has the highest possibility of occurrence). And the same is repeated , production of F2 offsprings with 50% possibility of heterozygous individuals.So getting a homozygous dominant individual is very less likely to happen.

My question, is inbreeding really efficient at producing homozygosity?