Slow COUNT(*) with JSON_SEARCH - mysql

Question

I have a table that stores tags in the JSON format for each page. Current table has about 1,000,000 records.
When I run
SELECT COUNT(*) FROM alltags WHERE tagtype = 'pages' AND JSON_SEARCH(tags, 'one', 'Hampden') IS NOT NULL;
the query takes about 20 seconds
+----------+
| COUNT(*) |
+----------+
| 23500 |
+----------+
1 row in set (19.20 sec)
The query is slow regardless if I use InnoDB or MyISAM engine.
I got indexes for tagtype, tags and tagtype with tags columns. I need the exact number of results for pagination. Is there a way I can speed up the SELECT COUNT query? Selecting actual data is pretty instant.
SELECT id FROM alltags WHERE tagtype = 'pages' AND JSON_SEARCH(tags, 'one', 'Hampden') IS NOT NULL LIMIT 0,10;
+------+
| id |
+------+
| 5072 |
| 5075 |
| 5078 |
| 5081 |
| 5084 |
| 5087 |
| 5090 |
| 5093 |
| 5096 |
| 5099 |
+------+
10 rows in set (0.01 sec)
These are the indexes
SHOW INDEX FROM alltags;
+---------+------------+-----------+--------------+-------------+-----------+-------------+----------+--------+------+------------+---------+---------------+
| Table | Non_unique | Key_name | Seq_in_index | Column_name | Collation | Cardinality | Sub_part | Packed | Null | Index_type | Comment | Index_comment |
+---------+------------+-----------+--------------+-------------+-----------+-------------+----------+--------+------+------------+---------+---------------+
| alltags | 0 | PRIMARY | 1 | id | A | 896649 | NULL | NULL | | BTREE | | |
| alltags | 1 | tagtype | 1 | tagtype | A | 2 | NULL | NULL | | BTREE | | |
| alltags | 1 | keyword | 1 | keyword | A | 33 | NULL | NULL | | BTREE | | |
| alltags | 1 | tags | 1 | tags | A | 89665 | NULL | NULL | YES | BTREE | | |
+---------+------------+-----------+--------------+-------------+-----------+-------------+----------+--------+------+------------+---------+---------------+
EXPLAIN results:
Select data
EXPLAIN SELECT id FROM alltags WHERE tagtype = 'pages' AND JSON_SEARCH(tags, 'one', 'Hampden') IS NOT NULL;
+----+-------------+---------+------------+------+---------------+---------+---------+-------+--------+----------+-------------+
| id | select_type | table | partitions | type | possible_keys | key | key_len | ref | rows | filtered | Extra |
+----+-------------+---------+------------+------+---------------+---------+---------+-------+--------+----------+-------------+
| 1 | SIMPLE | alltags | NULL | ref | tagtype | tagtype | 7 | const | 892372 | 100.00 | Using where |
+----+-------------+---------+------------+------+---------------+---------+---------+-------+--------+----------+-------------+
1 row in set, 1 warning (0.00 sec)
Select count
EXPLAIN SELECT COUNT(*) FROM alltags WHERE tagtype = 'pages' AND JSON_SEARCH(tags, 'one', 'Hampden') IS NOT NULL;
+----+-------------+---------+------------+------+---------------+---------+---------+-------+--------+----------+-------------+
| id | select_type | table | partitions | type | possible_keys | key | key_len | ref | rows | filtered | Extra |
+----+-------------+---------+------------+------+---------------+---------+---------+-------+--------+----------+-------------+
| 1 | SIMPLE | alltags | NULL | ref | tagtype | tagtype | 7 | const | 892372 | 100.00 | Using where |
+----+-------------+---------+------------+------+---------------+---------+---------+-------+--------+----------+-------------+
1 row in set, 1 warning (0.00 sec)