What is the Protestant view of communal living?

I can't find any teaching that would prohibit communal living, yet it seems so rare.
Is there a specific reason for this?

TL;DR:
Two specific reasons:

• There are few teachings because Christians don't criticise governments and politics.
• True communal living is rare because in practice it tends to fail due to human nature.

Communal living (and socialism, communism, etc.) are social and political concepts. Christians respect authority, obey the laws, and follow the customs of whatever society they happen to be living in (except when it would violate one of God's laws), so it would be inappropriate for Christian organizations to express negative views on such issues.

Submit yourselves to every ordinance of man for the Lord's sake: whether it be to the king, as supreme; Or unto governors, as unto them that are sent by him for the punishment of evildoers, and for the praise of them that do well.
— 1 Peter 2:13,14

This is especially true with respect to communal living, since, because of the large early conversions described in Acts 4, some of the Christians lived communally for a short time, supporting the converts that had come from far away and were financially unprepared to stay in Jerusalem for so long.
(See my answer to For how long did the early Christians share all their possessions?.)

Historically though, some individual Christian groups have deliberately tried communal living, but nor surprisingly, with disastrous results.

The most famous of these is the American Pilgrims who, about 400 years ago, tried communal farming.

The “common property” approach killed off about half the settlers. Governor Bradford recorded in his diary that everybody was happy to claim their equal share of production, but production only shrank. Slackers showed up late for work in the fields, and the hard workers resented it. It’s called “human nature.”

— Why the Pilgrims Abandoned Common Ownership for Private Property.

What is the Protestant view of communal living?

Not all Protestant are against this ideal of living lifestyle. Although practiced in the Early Church as seen in the Acts of the Apostles to some degree, many are not in favour of it too.

There are some Protestants who still practice this to one degree or another. More and more Protestant communities are doing this.

Anglican Protestantism has monks who live in monasteries.

Between 1841 and 1855, several religious orders for women were begun, among them the Community of St Mary the Virgin at Wantage and the Society of Saint Margaret at East Grinstead. Religious orders for men appeared later, beginning in 1866 with the Society of St. John the Evangelist or "Cowley Fathers". In North America, the founding of Anglican religious orders began in 1842 with the Nashotah Community for men in Wisconsin, followed in 1845 by the Sisterhood of the Holy Communion under Anne Ayres in New York.

In recent decades, there has been a remarkable growth of religious orders in other parts of the Anglican Communion, most notably in Tanzania, South Africa, the Solomon Islands, Vanuatu and Papua New Guinea. There are currently about 2,400 monks and nuns in the Anglican communion, about 55% of whom are women and 45% of whom are men.

Anglican religious order

The Taizé Community which started in France does this same thing with a slightly different variation.

The Taizé Community is an ecumenical Christian monastic fraternity in Taizé, Saône-et-Loire, Burgundy, France. It is composed of more than one hundred brothers, from Catholic and Protestant traditions, who originate from about thirty countries around the world. It was founded in 1940 by Brother Roger Schütz, a Reformed Protestant. Guidelines for the community's life are contained in The Rule of Taizé written by Brother Roger and first published in French in 1954.

Taizé has become one of the world's most important sites of Christian pilgrimage, with a focus on youth. Over 100,000 young people from around the world make pilgrimages to Taizé each year for prayer, Bible study, sharing, and communal work. Through the community's ecumenical outlook, they are encouraged to live in the spirit of kindness, simplicity and reconciliation. The community's church, the Church of Reconciliation, was inaugurated on 6 August 1962. It was designed by a Taizé member and architect, Brother Denis. Young Germans from Action Reconciliation Service for Peace, created for reconciliation after World War II, assumed the work of building it. Owing to the founder's commitment, since its inception the community has evolved into an important site for Catholic–Lutheran ecumenism. A Catholic, Brother Alois, succeeded as prior after his predecessor's death in 2005.

Taizé has become one of the world's most important sites of Christian pilgrimage, with a focus on youth. Over 100,000 young people from around the world make pilgrimages to Taizé each year for prayer, Bible study, sharing, and communal work. Through the community's ecumenical outlook, they are encouraged to live in the spirit of kindness, simplicity and reconciliation. The community's church, the Church of Reconciliation, was inaugurated on 6 August 1962. It was designed by a Taizé member and architect, Brother Denis. Young Germans from Action Reconciliation Service for Peace, created for reconciliation after World War II, assumed the work of building it. Owing to the founder's commitment, since its inception the community has evolved into an important site for Catholic–Lutheran ecumenism. A Catholic, Brother Alois, succeeded as prior after his predecessor's death in 2005.

Taizé Community