Just a quick note that when you ask about convents, you're specfically asking about women becoming nuns - men would become monks at monasteries.

Part of the reason is that while monasteries and convents provided for communal, ascetic lifestyles, these were not charitable operations for the poor. Monasteries and convents actually owned their own property and even their own serfs in 18th century Russia, and were economically supported through those means.

Another point of note is that the Russian Orthodox Church in particular faced a great deal of state control in its organization and operation, and this extended to monasteries and convents. Peter the Great (who in fact abolished the position of Patriarch of the Russian Orthodox Church, which would not be restored until 1917), passed a series of reforms to attempt to limit the growth of monasteries and convents, and to control their operation. Specifically for convents, this involved rules for strict enclosure, communal living, and restricting monastic vows to women between 50 and 60 years of age. Convents were expected to teach handicrafts, provide care to widows and orphans (with an emphasis on those related to clergy or military veterans), and the maintenance of hospitals. In short, nuns were expected to provide charity to those in need, rather than for the life of a nun to be an act of charity.

These reforms (like so many central reforms in Russian history) had very limited impact, but they established a principle that the Russian government had authority over the operation of monasteries and convents. Catherine the Great also promulgated a series of reforms in 1764, taking monastic property under state control (the monasteries were to be given a stipend based off of the proceeds collected). The number of monasteries and convents was drastically reduced, the number of monks and nuns for each institution was fixed, the rules of strict enclosure, communal living, and no vows for women under 50 was reiterated, and an additional rule was provided that any new monastery or convent needed explicit state approval to operate.

It's worth noting that in this period, a nun in a convent was actually expected to be maintained financially in some form, rather than relying on the convent to provide for all her needs. This was often provided from a variety of sources, such as a "dowry" paid to the convent by her parents, from income from personal property, from income earned by her own labor, by donations raised by local patrons, parish members, or relatives, or occasionally by modest state pensions.

As can be seen, the age at particular monasteries in this period tended to skew old (50 and above), and many nuns were in fact widows, who even might be attended by daughters or personal servants. Such women were mostly daughters or widows of the clergy, townsmen, civil or military servicemembers, or regular soldiers: all relatively elite groups in a country that was perhaps 90% peasants, most of whom were in serfdom. This last fact is important as well: a peasant could be living in dire poverty, but would not have the legal right to leave the land or service that he or she was bonded to for a monastic life.

Interestingly, from about 1800 until 1917 there was a revival and increased popularity of monastic orders in Russia, with the vast majority of such individuals taking vows being women. There was actually a push by female members to found new convents, and increase the number of nuns in existing convents, as well as a push to reorganize convents' finances in such a way that members were actually communally provided for, rather than being older women of independent means. There was even a convergence between women in convents and so-called derevenskie monashki, or "country nuns", who were unmarried peasant women living ascetic and pious lives in their villages, and supporting themselves through handicrafts. This latter movement in particular became more popular in the late 19th and early 20th centuries. Indeed, many of the former communities in the 19th century started as informal groups, or "almshouses", often existing for decades in this status before being formally recognized as convents. There in fact was an increase in the number of peasant women joining convents after 1861, when serfdom was abolished, and increasing mobility and increasing options for personal choice seemed to have played a role (along with piousness and negative personal circumstances) in attracting larger numbers of such women to convents. However, even with the increasing popularity of such a lifestyle, it should be noted that by 1914 we're talking about a total Russian monastic population of less than 100,000 (including 11,845 monks, 9,485 male novices, 17,283 nuns, and 56,016 female novices in 550 monasteries and 475 convents). It was still a relatively elite lifestyle for the few, rather than an option for the vast majority.

Source: Wagner, William. “The Transformation of Female Orthodox Monasticism in Nizhnii Novgorod Diocese, 1764–1929, in Comparative Perspective.” The Journal of Modern History, vol. 78, no. 4, 2006, pp. 793–845. Available here.