They seem necessary to modern "indult", irregular celebrants of the pre-Conciliar Latin rites who say no variation of these prayers in English or Latin throughout the week. Lavabo inter innocentes manus meas or Lava me Domine?
Altar cards are something of an anomaly, if only because they pertain to prayers by the priest that were once private devotions, with the exception of the Gloria and Creed. Moreover, these prayers, personal in origin, varied considerably across the Latin Church. The dual offering of the bread and the chalice is unique to south, central Europe. Northern and far Western Europe preferred the single offering with the paten sitting on top of the prepared chalice. One presumes that with enough repetition and decent command of the Latin language one might eventually learn the Offerimus tibi and the Placeat within a few weeks.
I recall reading somewhere, but cannot recall where, that the Tridentine Missal of St Pius V (the actual one, not everything from Trent to '64) only mentions the central card and says that it may rest against the Crucifix. Tabernacles did not occupy the central place of the main altar yet; a great many were simple holes in the wall, which Trent addressed. The Caeremoniale episcoporum directs that if a bishop is to pontificate at an altar where the Sanctissimum is reserved, it is to be removed to another altar. Presumably, priests were saying their Office regularly enough to memorize psalm 25 and the medieval practice was to recite St. John's prologue during the return to the sacristy. Even after Trent many Gallican usages describe the celebrant reciting the Last Gospel, if it is not proper, during the return to the sacristy at high Mass; the familiar Roman recitation at the altar was reserved to low Mass only. Archbishop Lefebvre was once accused of modernism for "skipping the Last Gospel" when in fact he followed the rubrics of episcopal ceremony by reciting it during the recession. Could the received Roman practice of saying it at the altar at the end of high Mass be inaccurate? Could it still have been said the medieval way at high Mass until the invention of the outside cards?
I never understood why the cards were necessary before the changes to the ordo Missae of the 1960s. Still, they have utility for the modern, occasional celebrant.