One thing to keep in mind is that ecclesiastical possessions might predate the Carolingian political order (that is to say, the 9th century political organization of what is now France, Germany, and Italy) and the clergy was not an institution running parallel to political power, but rather closely integrated with political power and indeed a major determinant of political decisions and ideology. From about the sixth century up to about the investiture controversy, a local political authority might commonly be synonymous with the local bishop. Indeed, in many ways the post-roman transformation had eliminated a strong secular negotiating party and the political order which subsequently emerged was disfavored in the negotiated non-linear power relationship between political and religious authority.

What this means is that in the relationship between Carolingian government organization and clergy, while still largely non-linear and characterized by fluctuating and varying agreements between monarchy and church institutions, was nonetheless largely characterized by an enormous delegation of the general government administration to ecclesiastical institutions.

It's also worth pointing out that the Carolingian cultural heritage largely came from the Europe's Latin sphere (albeit from the periphery of that sphere) and this meant that the Empire's eastward expansion into Germanic terretory necessitated the top-down imposition of an authority system they understood. While this could include the establishment of ecclesiastical institutions, the carolingians principally preferred the construction of secular systems of government. The Carolingian expansion westward and southward, on the other hand, saw them impose themselves on authority structures they already recognized. In these parts of the empire, while we always see "high offices" (the "Margraves") appointed to secular officials as elsewhere in the Empire, where we see the Carolingian bestowing lower-level imperial offices like Procurator (although they seem to have been fairly inconsistent in using specific titles) the Carolingians instead lean on preexisting institutions, often ecclesiastical ones. The carolingians even use the Latin phrase Res Pubblica in their written explanation of authorities they are delegating, and even if their application of the phrase was different than how it was applied during the Roman period centuries prior, this and other appropriation of longstanding terminologies and legal constructs demonstrates they were satisfied to lean on institutions which they found already in place. Indeed, even in their earliest period of conquest of Italy in particular, the Carolingians seem particularly unwilling (or unable) to substitute ecclesiastical authorities, even in important economic and political centers of power. In short, these ecclesiastical institutions often predated (and outlasted) the Carolingians, and the formal delegation of public functions to these institutions contributed to their growth.

Did bestowing government responsibilities onto abbots and bishops come with increased grants of land? Not really, although they could use their new authorities to accumulate more property. And the general point is that the power of the religious institutions predated the Carolingians.

Without more specific information as to which specific donations you might be referring to (and maybe you're actually referring to England, which while more linked to Latin cultural heritage than many might think does have its own dynamics at play) I unfortunately can't deliver more specific information.

I have the kindle edition of the Cambridge History of Medieval Europe 1911 edition as a searchable online book and chapter IV of volume 1 is on the Merovingians. This is 100-200 years before your selected time, but discusses the emergence of new forms of land ownership at this time. Land donation was complex and could be for life, or heritable but the church was a one way donation. Church lands did not routinely get freed up or sold. However the church also needed land to be productive, and so in turn made for-life grants of land to mutual benefit. Knights needed productive land holdings to meet their military obligations, and the Merovingians were seeking permanently armed horse. There was a very high degree of superstition and belief, and the Merovingians were a pretty sordid violent lot, with a good reason to fear their afterlife. Donation of land, acts of piety offset this risk. And, the church backed friends. It was a third estate between the emerging monarchy and the vassals, and had protecting powers over the poor, widowed, indigent and captives of war. It was politically useful to support the church.

So land came into the possession of the church as acts of pious donation, and as cynical offset of bad deeds, and for pragmatic benefit. During this time land possession came into more formal definition and kings followed the church model of giving for-life grant of use, rather than heritable absolute possession.

As it says in Chapter IV the eleventh century fief is the direct descendant of the eighth century benefice

Charles Martel had the ability to direct benefice of church lands: he didn't need to own the land, to direct how the church made grant of use. The church needed him as much as he needed them: they followed his instructions.