I've never bought the oft-asserted maxim that said is somehow transparent to the reader. More than three saids in a row sets up an annoying monotony that never fails to pop me out of the narrative.
Demonstrably false is the claim that using tags other than said or asked , or adverbs in a tag, brands a writer as an amateur, doomed to financial failure and suffering endless derision by their literary betters.
In Clawback, J. A. Jance goes hog wild with tag verbs: asked, added, admitted, advised, agreed, allowed, answered, asked, assured, began, called, called after, cautioned, chimed in, commanded, corrected, croaked, declared, demanded, echoed, explained, groused, growled, grumbled, inquired, insisted, interjected, managed, muttered, nodded (!), observed, ordered, pleaded, repeated, replied, returned, said, smiled (!), sneered, sniffed (!), sobbed, suggested, told, urged, whined, whispered, and that's just from a random sampling.
In Harry Potter and the Philosopher's Stone, J. K. Rowling uses these tags: said, told, muttered, whispered, called, snapped, added, murmured, mumbled, began, snarled, suggested, reminded, moaned, shouted, explained, stammered, warned, screamed, sighed, repeated, agreed, grunted, yelled, groaned, admitted, wondered, pressed, hissed, smiled(!), sobbed, whined, ordered, lied, cried, wailed, confessed, declared, interrupted, bellowed, grumbled, observed, replied, choked out, howled, urged, advised, pleaded.
77% of that book's tag verbs are "said", but by no means all.
Generally I agree that every ms could benefit from a merciless tag-ectomy pass during revision. But spoken delivery cannot always be implied in plaintext or cliched gesture or facial expression. Often a writer can justifiably economize by allowing a character to be expressive with a non-said verb, a "!", and even (gasp!) a dreaded adverb:
“Red card!” said Dean furiously.
“Watching — spying — might be following us,” muttered Uncle Vernon wildly.
“I wish I knew what this means!” he burst out angrily.
Harry sprang toward the flame door, but Voldemort screamed “SEIZE HIM!”
“All yours,” smiled Hagrid.
“Come here,” Quirrell repeated.
When they shook their heads, he wailed, “I’ve lost him! He keeps getting away from me!”
Good enough for J.K. and her billion readers, good enough for me and mine.
BTW HPatPS was Rowling's debut novel. Clearly her agent, editors, and publisher did not object to her liberal use of non-said tag verbs.
I submit that the OP's agent was merely parroting what "respectable" authors and opinionators assert concerning the hallmarks of good vs. crummy writing.