These amendments were not drafted by amateurs. They were drafted by professional politicians who understood how how courts and legislatures actually work. They felt that the Fifteenth Amendment was required because they really wanted black citizens to be able to vote. And they knew that legislators in some of the states would do all that they could to prevent the enfranchisement of blacks, no matter what the Fifteenth Amendment might say.
A state doesn't have to expressly prohibit blacks from voting in order to prevent or discourage them from voting. There's lots of other ways that are quite effective. A state might decide to just not have any polling places within black communities and require that blacks who wish to vote travel to neighborboods that are inconvenient or unsafe for them to be. See how many ways you can come up with to discourage blacks from voting without enacting an express prohibition of black voting.
Because that is exactly what happened. As the Court pointed out in South Carolina v. Katzenbach (1966):
"Meanwhile, beginning in 1890, the States of Alabama, Georgia, Louisiana, Mississippi, North Carolina, South Carolina, and Virginia enacted tests still in use which were specifically designed to prevent Negroes from voting. Typically, they made the ability to read and write a registration qualification and also required completion of a registration form. These laws were based on the fact that as of 1890 in each of the named States, more than two-thirds fo the adult Negroes were illiterate while less than one-quarter of the adult whites were unable to read or write. At the same time, alternate tests were prescribed in all of the named States to assure that white illiterates would not be deprived of the franchise. These included grandfather clauses, property qualifications, 'good character' tests, and the requirement that registrants 'understand' or 'interpret' certain matter."
The professionals who drafted the Fifteenth Amendment knew that some of the states would attempt to evade the Fifteenth Amendment even if they could not foresee precisely how the evasions might be designed. And that's why we have section 2, which authorizes Congress to enact "appropriate" legislation to enforce the amendment.
But that's just not what enforcement means. It only means establishing the procedures to see to it that the subjects of the law comply with the law itself, not with the "intent" behind the law. I mean, I've always considered it an elemental principle of law - one that doesn't even need to be stated - that if the law says "Don't do X," then you have a right not to be bothered by anyone if you refrain from doing X. You shouldn't have to constantly be asking yourself, "OK, now why don't they want me doing that? Am I truly fulfilling its purpose?" Say they outlaw working for wages on Sundays, and then you decide to do volunteer work on that day, devoting nearly the whole day helping out at the local hospital or library or whatever, and then the authorities come up to you and start chewing you out, saying you're working way too much, and you say, "But it's volunteer work, the law only prohibits wage work," and they say, "Yeah, but the idea was to get you to work less, not more!" you would be entirely justified in saying, "BUT THAT'S NOT WHAT THE LAW SAYS!!!"
The 15th amendment does not say that states must have "reasonable" voting qualifications, and it does not say that Congress shall have the power to make sure that everyone gets a fair shake at being able to vote; it specifically says that states shall not use race as a criterion in awarding the franchise, and it gives Congress the power to make sure that they don't. It really couldn't be any clearer than that.