People without vows who maintain a celibate lifestyle could be considered householder brahmacaris. Also, many people don't realize that it is possible to take a vow of celibacy and remain as a householder within our Tibetan tradition, such a person is known as a full genyen.
These are just ecclesiastical definitions that have little bearing on the actual purpose of renunciation. The purpose of being a "monk" in Buddhism is not to undergo a formal ordination ceremony and be certified as having "left the home life" by institutional authorities. The Buddha didn't formulate such conventions, let alone insist on everyone having vows and being classified as X kind of renunciate. There were plenty of disciples who just showed up and were welcomed as bhikṣu-s.
The bizarre thing is that the vows we cherish so much now are just house rules laid down because, apparently, some monks and nuns screwed up in the past and caused a disturbance. Svagata got wasted, vomited all over himself and passed out in front of the Buddha (or outside the park gate depending on the version of the story), hence there was a rule laid down against alcohol, which later became a fossilized precept; ordination thereafter required that you vow not to consume any alcohol.
So these vows that you insist are so important were formulated because people behaved foolishly. Nuns vow not to cross a bridge with a monk because some silly nun started shaking a rope bridge one day and poor Mahākāśyapa fell into the river (this is probably pure fiction, but who knows).
Is that really so sacred that it requires a sacred vow? Can't we just cut that out since it seems pretty irrelevant and childish?
Ven. Indrajala within the Mulasarvastivada literature, especially Kunkyen Tsonawa's commentary on the Vinaya, there is a great amount of detail about the function of the ordination and various people who perform it. I would imagine you find this in the Dharmagupta as well, and certainly it is a huge topic of discussion (and sometimes contention) in the Theravada world.
I've translated two thick books on the subject of the Vinaya and studied it for my own purposes, too. My conclusion is that I agree with Jizang that the Vinaya is for people with "dull roots".
That doesn't mean we do away with the śramaṇa lifestyle. No, we just recognize that renunciation and the śramaṇa lifestyle are completely different from Vinaya-based monasticism.
I would argue that the procedural nature of the Vinaya came about due to the conditions of India in addition to the bad behaviour of some of the early disciples of Lord Buddha.
Humans solve problems through increasing complexity. The Vinaya literature was a result of increasing complexity to address problems that were arising, probably with the shift towards landed monasticism and dependence on middle-class and up benefactors who demanded the image of purity as a condition for making offerings.
That being said, human societies and communities seldom voluntarily sacrifice complexity. This is what makes simplification, even when it is sensible, so difficult.
In India while there are some Hindus who find some of the loosely organized Sadhus inspiring, most families trust their offerings for renunciates to the organized monastic movements such as the Ramakrishna Mission, Swaminarayan BAPS movement, ISKCON and other Gaudiya organizations, etc.
Again, it is the image of purity that matters. You know as well as I do that what goes on behind closed doors in religious communities can be pretty dark and disagreeable, yet outwardly they project purity. This is to ensure that the offerings continue coming. The benefactors get a religious high from making offerings to a community they think are pure and holy.
The system works, sure, but then it is dishonest at a certain level.
As we just finished discussing earlier, Bhutanese monasteries are making condoms freely available. Clearly the Vinaya system isn't working there. Is it the fault of the system? No, but the existence of laws does not necessarily mean that people stop behaving in disagreeable ways. Peer pressure is a better tool for that purpose.
A bunch of self-proclaimed renunciants running around is not necessarily a good thing.
A bunch of formally ordained monks in Bhutan needing condoms to stop STD transmission (including HIV) is not necessarily working out so well, either. You hear horror stories from elsewhere, too. Wait until Asia's youth are empowered enough to start criticizing sacred religious institutions.
In the early days even Mahākāśyapa complained that the rules were not really working with new disciples. Having rules and punitive measures doesn't necessarily deter everyone from misbehaving. Having a common, rational and consensus-based system is far superior. This means that people come together for their mutual interest, as was the case in the early sangha. It means the rulebook can be updated and revised accordingly, as the Buddha suggested.
Personally I'm in favour of minimalist procedures and rules. If you need a vow against having sex to remain celibate, then clearly you're not really interested in being a śramaṇa from the start. If you need a vow to stop yourself from committing homicide, then you probably shouldn't be living as a monk in a religion based around non-violence. In a centralized authoritarian style of monastic system, you need clearly defined rules and regulations, like in the case of Bhutan: you can't technically force someone to disrobe if they thigh hump someone. You can only force them to disrobe if they penetrate an orifice. Realistically such people should be encouraged to go home.
This again is a fault of large scale institutions. If you had small decentralized communities, then it would be pretty easy for the leader or community as a small whole to politely encourage such members to leave without having to defer to the fine points of ecclesiastical law.
I believe my anarchist inclinations are coming through here.