In the Roman Catholic Church, ordination is 'Holy Orders,' a sacrament that leaves an indelible mark on the soul of the recipient. It must be carried out by a Bishop who is in a line of apostolic succession that purportedly dates back to Christ and his apostles. Martin Luther thought that through and decided it didn't make sense, particularly in cases where Christians were hauled off in chains as slaves to Muslim lands or otherwise separated from the universal church. He reasoned that the Christians could select by vote the one they considered most qualified (had to be a man though) and appoint that one as a minister capable of administering baptism and the Lord's supper. Other Protestant churches descending from the Reformation reached the same conclusion, with some having ordination as a responsibility of the ecclesiastical hierarchy, and others leaving it to a vote of the local church (as it was in my case).
In the mid-20th century a man named Kirby J. Hensley used the freedom of religion available in the United States to start his own church and issue ordinations for free, though there was a fee for people to pay to receive a printed certificate by mail. His church ran ads in the backs of magazines for years, ordaining anyone who asked. The legitimacy of his church and its ordinations were fought out in court for years before finally it was established that the government cannot be the judge of what is a valid religion and what is not. Now, with the exception of Tennessee, ministers ordained by a branch of the Universal Life Church are able to officiate weddings legally throughout the United States. Tennessee passed legislation a few years ago specifically invalidated weddings carried out by ministers ordained through the internet, though frankly I don't see how that law can possible remain on the books given how it violates religious freedom by determining what kind of religious practices are unacceptable.
What does ULC or any other 'online ordination' actually accomplish? Other that providing people the legal standing to officiate weddings and sign marriage licenses, not much. They are also given the same protections and responsibilities around pastoral privacy that all other ministers have. Beyond that, really anyone can organize religious rituals like baptisms, baby namings, funerals, and whatever else with or without ordination. The law really isn't involved in such matters of religious practice.
If ordination accomplishes so little, then why do churches and other religious organizations still bother with it? That is, they could easily issue a document to whoever they want to officiate weddings and call it a day, without the need for significant ministry education or any ceremony to recognized the ordinand. It's not just about a legality, of course, and that's what makes the difference.
In the Unitarian Universalist Association of Congregations the practice is to have local congregations sponsor whoever they want to have ordained, and the individual then goes through a process set forth by the Ministerial Fellowship Committee. It's a long process that includes criminal background checks, completing an MDiv or equivalent approved course of study, a unit of Clinical Pastoral Education, and an internship. Once the person has passed all that an various interviews, they may be recommended for preliminary fellowship. Assuming the Unitarian Universalist Ministers Association accepts, the candidate can then be ordained by the sponsoring congregation and received into fellowship by the UUMA.
As I said, it's a long process. It's costly and time consuming to answer a call to ordained ministry within Unitarian Universalism, and what is missed in that description is what really sets ordination in such a scenario apart from easy online ordination. It's not just the requirements for preparation. It's the relationships and ministry that are formed along the way.
So far I have attended two UU ordinations. One was more Christian-leaning, and the other was centered more on the candidate's social justice ministry. In both cases they were surrounded by colleagues, professors, friends, family, and congregants as they were welcomed into ordained ministry. In this setting, ordination is very much an act of the community, and the ordinand has deep ties to the tradition not only in terms of theory, but in practice and especially in relationships.
That isn't to say that such is lacking in other traditions, by any means. In Roman Catholicism the bishop is the one who ordains, but the ceremony is attended by other clergy, family, friends, and parishioners. Along the way to receiving Holy Orders the candidate for priesthood has formed bonds with the tradition and its people, and these are expressed in and through the ritual that they consider a sacrament.
What I've described above is wholly lacking from 'online ordination.' It is perfectly fine to be ordained as such and start a wedding business or even a church. It just doesn't have the profoundly personal touch that a full-blooded ordination within a more traditional church body will provide. For the ULC and similar online ministries, ordination is simply a transaction that provides a certain legal status for limited purposes. There is no gathered congregation, and no sense of a major milestone shared among any people.
For those who seek ordination within Unitarian Universalism, the Roman Catholic Church, or any Protestant denomination it's not just about a legal formality. It is a matter of putting down roots and being recognized as a trustworthy person to embody and carry forward the faith tradition. Setting aside any spiritual considerations, which are invisible and unprovable, what we can see is a tangible expression in ordination of a sociological reality.
That's why ordination still matters.