What is the Catholic position on ethnic parishes today?

These "ethnic-language Masses", or more properly the groups to which they cater, aren't "sub-parishes" in any sense. A parish is defined by canon law:

A parish is a certain community of the Christian faithful stably constituted in a particular church, whose pastoral care is entrusted to a pastor (parochus) as its proper pastor (pastor) under the authority of the diocesan bishop.

(Code of Canon Law, Canon 515 Sec. 1)

In general, a parish is the community of Catholics residing in a particular area; but there can be parishes erected by the bishop on the basis of common languages or cultural background:

As a general rule a parish is to be territorial, that is, one which includes all the Christian faithful of a certain territory. When it is expedient, however, personal parishes are to be established determined by reason of the rite, language, or nationality of the Christian faithful of some territory, or even for some other reason.

(Canon 518)

As you point out, it was historically the case that there were enough priests in an area that a bishop could create an ethnic-language and separate English-language parish covering the same geographic area. In most dioceses of North America, that is no longer the case. Yet Catholics still have the right to receive the sacraments, just as priests have the duty to provide them at reasonable places and times.

Of course, it is possible to receive the Eucharist, in particular, without understanding the language of the Mass at which it is consecrated. But since the Second Vatican Council attached great importance to saying the Mass in the vernacular, it seems appropriate to celebrate the Eucharist in locally predominant languages other than the national language, when that can be done. Those attending this Mass don't generally speaking constitute a parish proper; they're parishioners of the local parish and other parishes who gather for a Mass in their native tongue. Residents of other (geographic) parishes who attend these Masses do not become members of the parish at which this Mass is celebrated; they remain members of the parish where they live.

Catholics are obliged to attend Mass every Sunday unless they are ill or have some other grave reason for failing to attend. Being unable to understand the primary language in which Mass is celebrated doesn't constitute a grave reason, so that Catholics are obliged to attend weekly Mass even if it's not the Mass in their preferred language.

My church (Roman Catholic, on the south coast of the UK) hosts a monthly Mass in Polish, which is well attended. The building was packed for the Polish "Midnight" Mass at Christmas.

It also hosts a weekly (Sunday afternoon) Mass for the Ordinariate congregation, whose members are not members of the local diocese.

In all these efforts, including the Hispanic Masses you reference, I would like to think that the Church is not just seeking to get people in the door, but providing a ministry. It is to be hoped that immigrant churchgoers will seek to assimilate themselves into the local culture, and there is at least a weekly opportunity to attend Mass in English, which would fulfil an obligation. But such assimilation may take some considerable time. If the Church can provide the opportunity for confession and Mass in a native language, and allow full participation in the rites of Church, then why not?

[The answer to Why not is, of course, your point about making fully-fledged parishioners. However in our case, it's quite likely that members of the Polish community are not long-term residents. We do have a sizable Italian Catholic community, and they do attend Masses in English.]