Why does sql server need to convert count(*) result into int before comparing it with an int variable?
The fact that you are comparing it against an integer variable is irrelevant.

The plan for COUNT always has an CONVERT_IMPLICIT(int,[ExprNNNN],0)) where ExprNNNN is the label for the expression representing the result of the COUNT.

My assumption has always been that the code for COUNT just ends up calling the same code as COUNT_BIG and the cast is necessary to convert the bigint result of that back down to int.

In fact COUNT_BIG(*) isn't even distinguished in the query plan from COUNT(*). Both show up as Scalar Operator(Count(*)).

COUNT_BIG(nullable_column) does get distinguished in the execution plan from COUNT(nullable_column)  but the latter still gets an implicit cast back down to int.

Some evidence that this is the case is below. 

WITH 
E1(N) AS 
(
    SELECT 1 UNION ALL SELECT 1 UNION ALL SELECT 1 UNION ALL 
    SELECT 1 UNION ALL SELECT 1 UNION ALL SELECT 1 UNION ALL 
    SELECT 1 UNION ALL SELECT 1 UNION ALL SELECT 1 UNION ALL SELECT 1
)                                       -- 1*10^1 or 10 rows
, E2(N) AS (SELECT 1 FROM E1 a, E1 b)   -- 1*10^2 or 100 rows
, E4(N) AS (SELECT 1 FROM E2 a, E2 b)   -- 1*10^4 or 10,000 rows
, E8(N) AS (SELECT 1 FROM E4 a, E4 b)   -- 1*10^8 or 100,000,000 rows
, E16(N) AS (SELECT 1 FROM E8 a, E8 b)  -- 1*10^16 or 10,000,000,000,000,000 rows
, T(N) AS (SELECT TOP (2150000000) 
                  ROW_NUMBER() OVER (ORDER BY (SELECT NULL)) AS N FROM E16)
SELECT COUNT(CASE WHEN N &lt; 2150000000 THEN 1 END)
FROM T 
OPTION (MAXDOP 1)


This takes about 7 minutes to run on my desktop and returns the following


Msg 8115, Level 16, State 2, Line 1
Arithmetic overflow error converting expression to data type int.
Warning: Null value is eliminated by an aggregate or other SET operation.


Which indicates that the COUNT must have continued on after an int would have overflowed (at 2147483647) and the last row (2150000000) was processed by the COUNT operator leading to the message about NULL being returned.

By way of comparison replacing the COUNT expression with SUM(CASE WHEN N &lt; 2150000000 THEN 1 END) returns 


Msg 8115, Level 16, State 2, Line 1
Arithmetic overflow error converting expression to data type int.


with no ANSI warning about NULL. From which I conclude the overflow happened in this case during the aggregation itself before row 2,150,000,000 was reached.