If Mendel's plant had had exposed reproductive structures, his work crossing the plants might have been confounded by pollinators, such as insects, pollinating the plants in a way in which he could not control. That would leave Mendel with no way to know what the parents of given seed were, making analysis of the results and the derivation of his laws impossible. His whole method relied on controlling the pollination of flowers.
Work Step by Step
To figure this out, first consider the nature pr Mendel's work: he was trying to find consistent laws of inheritance. To do any scientific experiment, you need clear control over all parts of the experiment so that you can make sense of things. If you are doing an experiment in chemistry and someone rearranges your test tubes, you will get a mess at best, and possibly a dangergous explosion. Exposed parts takes away Mendel's control of the crossing.