You mentioned that you'll be optimizing this legacy app.
One of the first, and easiest, things you can do to improve performance is remove all the BEGIN TRAN and COMMIT TRAN for the stored procedures that only do SELECTs.
Here is a simple test to demonstrate:
/* Compare basic SELECT times with and without a transaction */
DECLARE @date DATETIME2
DECLARE @noTran INT
DECLARE @withTran INT
SET @noTran = 0
SET @withTran = 0
DECLARE @t TABLE (ColA INT)
INSERT @t VALUES (1)
DECLARE
@count INT,
@value INT
SET @count = 1
WHILE @count < 1000000
BEGIN
SET @date = GETDATE()
SELECT @value = ColA FROM @t WHERE ColA = 1
SET @noTran = @noTran + DATEDIFF(MICROSECOND, @date, GETDATE())
SET @date = GETDATE()
BEGIN TRAN
SELECT @value = ColA FROM @t WHERE ColA = 1
COMMIT TRAN
SET @withTran = @withTran + DATEDIFF(MICROSECOND, @date, GETDATE())
SET @count = @count + 1
END
SELECT
@noTran / 1000000. AS Seconds_NoTransaction,
@withTran / 1000000. AS Seconds_WithTransaction
/** Results **/
Seconds_NoTransaction Seconds_WithTransaction
--------------------------------------- ---------------------------------------
14.23600000 18.08300000
You can see there is a definite overhead associated with the transactions.
Note: this is assuming your these stored procedures are not using any special isolation levels or locking hints (for something like handling pessimistic concurrency). In that case, obvously you would want to keep them.
So to answer the question, I would only leave in the transactions where you are actually attempting to preserve the integrity of the data modifications in case of an error in the code, SQL Server, or the hardware.