First, this is overtly not true. Reproducibility refers to all forms: that the paper figures can be built from code and don't have errors, that a reimplementation of new code on the same data produces the same results, and that gathering new data (e.g. by conducting the same experiment again if possible, in other words replication) produces comparable results.
Second, publishing code helps make invisible decisions visible in a far better manner than the paper text does. Try as we might to imagine that every single researcher degree of freedom is baked into the text, it isn't and it never has been.
Third, errors do occur. They occur when running author code (stochasticity in models being inadequately pinned down, software version pinning, operating system -- I had a replication error stemming from round-towards-even behaviour implementation varying across platforms). If you have access to the code, then it's far easier to determine the source of the error. If the authors made a mistake cleaning data, having their code makes it easier to reproduce their results using their exact decisions net of the mistake you fix.
Most papers don't get replicated or reproduced. Making code available makes it more likely that, at a minimum, grad students will mechanically reproduce the result and try to play around with design parameters. That's a win.
Source: Extensive personal work in open and transparent science, including in replication; have written software to make researcher choices more transparent and help enable easier replication; published a meta-analysis of several dozen papers that used both reproducing author results from author code, producing author results with code reimplementation, and producing variant results -- each step was needed to ensure we were doing things right; a close friend of mine branched off into doing replications professionally for World Bank and associated entities and so we swap war stories; always make replication code available for my own work.