Well, you can. But if you're just learning the language, you're going to struggle to find words that don't use a predictable one. And if you do stumble across one of those, and you use 个 instead, people may not even notice.
No one is out there watching to make fun of you if you count horses in 只 instead of 匹.
That is not something that will happen with measure words. Ignoring some grammar will limit you. This is not such a case. Ignoring semantics-free measure words will make you sound like a native speaker.
Chinese measure words are not something that happens on a noun-by-noun basis. Memorizing them as part of a noun is not a well-chosen approach. Most often this will saddle you with the burden of separately memorizing "pass" and "passed" as independent forms of the verb, while providing comparable benefits.
You might have noticed that my comment above suggested that
(a) the default measure word is 个;
(b) the default measure word for a horse is not 个.
No one is out there watching to make fun of you if you count horses in 只 instead of 匹.