5’10” won’t get someone ruled as short. It’s just not prototypical height. Catchers have arms and get block. They can typically play anywhere on the corner infield or outfield.
A 5’9” first baseman probably has another issue unless he can run and play outfield. He’s probably not a masher. A first baseman typically has to be a masher. Some teams don’t recruit first baseman. They figure the extra players who can hit can DH or play first.
A former teammate/friend’s son was recruited by a top ranked team as a shortstop. The junior shortstop didn’t leave in the draft as expected. A kid who was expected to play short played first for a season. He hit .340 with an .880 OPS. He followed up being an All American at short the following two years and a first round pick.
Teams generally recruit pitchers, catchers, middle infielders and center fielders. The middle infielders and center fielders (assuming they don’t throw left) can play anywhere. Anyone else better be able to mash.
Where the previously mentioned kid played the coach took a right fielder with a gun and turned him into a catcher. He never caught until college. He was just that athletic he could make the conversion. Three other recruited catchers started at first, third,* left and DH. The regular third baseman missed extended time one season with an injury. Two ultimately became starting catchers. One has been in the majors for several years. One stayed in left and was drafted as a power hitting corner outfielder.
The kid moved from right was drafted as a catcher. Bob Boone (Phillies, Angels) was a third baseman in college. He became a catcher in the minors. Blake Swihart (Red Sox, Dbacks) was a shortstop in high school and converted to catcher in the minors.
A catcher needs to be versatile. What if he gets to college and there are one or two better catchers on the team? Or the team brings in catchers in following years? Four years is a long time to catch bullpens.
The thing about catchers is a team will constantly recruit them. Chances are there will always be three on the roster. They will always be looking for new catchers since at least one of the three is likely to transfer. Regardless of position the coaching staff is always looking for someone better.
One of my son’s high school and travel teammates chose his dream school. It was a reach. He could only play first. He was 6’. He could pick it with anyone. He crushed the ball. But he didn’t elevate. He hit hard doubles. He sat behind two prototype 6’3” 210) 1B/DH’s until he was told Opening Day Eve of junior year his services would no longer be needed.
I had a kid on my 13u to 16u travel team who could pick it at first with anyone. But he was 5’8” and done growing at fourteen. He ran a 6.8. I told him in 14u he would start playing more outfield. I told him it was unlikely a coach would want him at first. A lot he could pick a taller first baseman could catch on the fly. I was right about the kid. He played left in high school and at a D3.